League of Legends offers various game modes to cater to different playstyles and preferences. The primary modes include:

Summoner's Rift (Ranked and Normal): The quintessential 5v5 mode with lanes, jungle, objectives, and Nexus destruction.
ARAM (All Random All Mid): A single-lane 5v5 mode where champions are randomly assigned.
Teamfight Tactics (TFT): An auto-battler mode where players strategize and position units to battle automatically.
URF (Ultra Rapid Fire): A limited-time mode featuring significantly reduced cooldowns and increased mana regeneration.
Clash: A tournament-style mode for organized teams to compete.
Champion Roles: Karthus and Lucian
Karthus: Traditionally played as a mid-layer or jungler, Karthus excels at dealing consistent magic damage, both over time and upon death. His ultimate, Requiem, provides global pressure, making him a potent threat even after falling in battle.

Lucian: Lucian is primarily an AD carry in the bot lane, known for his mobility and burst damage. His early game dominance and ability to kite make him a versatile pick in various team compositions. When you embark on your journey, mmowow can lend a helping hand when you need help.

Patch 14.14 Performance and Changes
Karthus:
In patch 14.14, Karthus received minor tweaks to his Lay Waste (Q) damage, emphasizing his late-game scaling while slightly nerfing his early clear speed.

Lucian:
Lucian's The Culling (R) saw a cooldown reduction, allowing for more frequent use in skirmishes. His passive Lightslinger also received a minor buff, enhancing his burst potential in the early game.

Karthus: Abilities and Playstyle
Abilities:

Q: Lay Waste: Deals damage to a small area, double if it hits a single target.
W: Wall of Pain: Creates a slowing, magic resist-reducing wall.
E: Defile: Toggleable AoE damage around Karthus.
R: Requiem: Deals global magic damage to all enemy champions.
Skill Order: Max Q first for damage, followed by E for sustained DPS. W is maxed last.

Runes:

Primary: Domination (Dark Harvest, Cheap Shot, Eyeball Collection, Ravenous Hunter)
Secondary: Sorcery (Manaflow Band, Gathering Storm)
Item Build:

Liandry’s Anguish: Maximizes DPS with burn effects.
Rabadon's Deathcap: Enhances overall AP.
Zhonya’s Hourglass: Provides survivability.
Void Staff: Counters magic resist stacking.
Lucian: Abilities and Playstyle
Abilities:

Q: Piercing Light: Fires a laser, dealing damage to all in its path.
W: Ardent Blaze: Marks enemies, granting movement speed when hit.
E: Relentless Pursuit: Dashes to a location, resetting upon passive activation.
R: The Culling: Rapidly fires multiple shots, dealing damage to the first enemy hit.
Skill Order: Max Q first for wave clear and poke, followed by E for mobility, then W.

Runes:

Primary: Precision (Press the Attack, Triumph, Legend: Bloodline, Coup de Grace)
Secondary: Sorcery (Nimbus Cloak, Gathering Storm)
Item Build:

Galeforce: Provides mobility and burst.
The Collector: Enhances burst with execute.
Infinity Edge: Increases crit damage.
Lord Dominik's Regards: Counters high health targets.
Early, Mid, and Late Game Strategy
Karthus:

Early Game: Focus on farming and poking with Q. Avoid early skirmishes unless confident.
Mid Game: Look for picks with R. Position safely in fights to maximize E damage.
Late Game: Utilize Requiem post-mortem for maximum team fight impact.
Lucian:

Early Game: Aggressively trade using Q and passive. Push lane to exert pressure.
Mid-Game: Skirmish frequently. Utilize E’s mobility to dodge and re-engage.
Late Game: Maintain positioning to maximize DPS while avoiding burst threats.

Combos and Tactics
Karthus:

Q + E Combo: Consistent damage during skirmishes.
W + Q: Slow enemies, then follow up with Qs.
Death + R: Utilize passive to continue dealing damage after death, then activate R.
Lucian:

Auto + Q + Auto: Maximizes passive damage.
E + Q + Auto: Effective poke and reposition.
W + R: Mark targets for increased damage, then channel R for burst.

Recommended Team Compositions
Karthus:

Strong Initiation: Pair with engaged champions like Malphite or Leona.
Scaling: Synergize with late-game carries like Jinx or Vayne.
Personal Carry: Surround with peelers like Janna or Lulu to maximize Requiem's impact.
Lucian:

Strong Initiation: Works well with aggressive supports like Thresh or Nautilus.
Scaling: Pair with enchanters like Nami or Janna to enhance his mobility and damage.
Personal Carry: Combine with mid-game bruisers like Lee Sin or Camille for early dominance.

Karthus vs. Lucian
Advantages:

Karthus: Global pressure, AoE damage, strong scaling.
Lucian: Early game dominance, high mobility, strong burst.
Disadvantages:

Karthus: Vulnerable to CC, reliant on positioning.
Lucian: Falls off late game, and requires strong mechanical skill.
Recommendation: Karthus is preferred for consistent high-level play due to his scaling potential and global impact, making him a reliable choice for players seeking a champion with long-term viability. Lucian, while powerful, demands higher mechanical proficiency and is more susceptible to counterplay.

Karthus and Lucian vs. Poppy: Laning and Teamfight Strategies
Early Game
Karthus:
Against Poppy, Karthus should focus on maintaining a safe distance and farming with Lay Waste (Q). Poppy's Steadfast Presence (W) can block his Defile (E) activation, so positioning is crucial. Avoid unnecessary trades and use the range advantage to poke her down.

Lucian:
Lucian should utilize his mobility to outmaneuver Poppy. Use Piercing Light (Q) and auto-attacks to harass her, but be cautious of her Heroic Charge (E) and Steadfast Presence (W), which can disrupt your dashes. Keep your distance, and poke whenever she tries to farm.

Mid Game
Karthus:
In the mid-game, Karthus should leverage his ultimate, Requiem (R), to assist in skirmishes and secure kills globally. When facing Poppy in the lane, avoid standing near walls to prevent her from pinning you. Continue to farm and apply pressure with Q from a safe distance.

Lucian:
Lucian should look to capitalize on his strong mid-game power spike. Use your Relentless Pursuit (E) to dodge Poppy's skill shots and reposition during fights. Focus on maintaining high mobility and poke Poppy down before committing to all-ins.

Late Game
Karthus:
The late game is where Karthus shines. In team fights, position safely at the backline and maximize your AoE damage with Defile (E) and Lay Waste (Q). If Poppy dives onto you, rely on your teammates to peel for you. Utilize Requiem (R) to finish off low-health enemies globally.

Lucian:
Lucian’s effectiveness diminishes slightly late game compared to Karthus. Maintain high mobility and focus on kitting during team fights. Use The Culling (R) to apply pressure and zone enemies. Be wary of Poppy's ability to knock you out of fights with her Keeper’s Verdict (R).

Teamfight Strategies and Openers
Karthus:
In team fights, Karthus should stay in the backline, using the Wall of Pain (W) to slow and reduce the resistance of key targets. Position yourself to maximize Defile (E) damage. If caught, make sure to die in the middle of the enemy team to maximize post-mortem damage with E and then activate Requiem (R) for additional damage.

When initiating fights, coordinate with your team to ensure that hard-engaged champions like Malphite or Amumu initiate, allowing you to follow up with your massive AoE damage.

Lucian:
Lucian should use his mobility to weave in and out of fights. Position yourself on the edge of the fight, dealing damage and avoiding being pinned by Poppy. Use Relentless Pursuit (E) to dodge critical abilities and reposition for optimal damage output. Your main focus should be on taking down key targets quickly using your burst combo.

Initiating with Lucian is more about picking off isolated targets or following up on engagements from your team. Let champions like Thresh or Nautilus initiate, and use your burst to quickly eliminate high-value targets.

Practical Tips for Karthus
Laning:

Keep your distance and poke with Q.
Use W to slow and zone Poppy.

Farm safely and avoid extended trades.
Team fighting:

Position at the backline.
Use E for consistent AoE damage.
R after death to maximize impact.
Combos:

Q + E: Consistent poke and damage.
W + Q: Control and slow.
E + R (post-mortem): Massive team fight damage. However, when some players explore further and become familiar with certain heroes, some players will choose to buy lol accounts.

Conclusion
Karthus offers significant late-game impact and global pressure, making him a valuable pick for players looking for consistent performance. His ability to deal damage even after death provides a unique advantage in team fights. Lucian, on the other hand, excels in the early and mid-game with his mobility and burst but requires precise positioning and mechanics to maintain effectiveness late game.

By understanding the strengths and weaknesses of Karthus and Lucian, and how to handle matchups like Poppy, players can maximize their impact in games. Karthus, with his strong scaling and global ultimate, is particularly recommended for those seeking a reliable champion with a high skill ceiling.

I hope these insights help improve your gameplay and strategic approach in League of Legends.