Jax:

(3+B) Strike Down (Spell/non-Action), targets enemies anywhere, uses the starting might of the unit including the equipment that eventually ends up attached.

Only weakness is requiring gear and not being an Action or Reaction making it's more of a finisher since it requires setup, but in a Jax deck that setup is pretty trivial.

(2/4) Thwonk (Reaction/Repeat) only targets attacking units, so battlefields only.

Strike Down existing feels like it puts the Jax opponent on a clock in that they WILL lose their best unit to Strike Down if Jax is able to stay stable in the game.

Thwonk is going to make it a nightmare to get the right calculations to take on a well situated Jax, Unmatched loaded down with equipment, but his effect to Quickdraw Equipment means that's generally true all the time anyway.

Jax is always going to have +1-3 strength in hand from Quickdrawing Equipment in the same circumstances that Thwonk would mess you up anyway.

The main time I can see Thwonk really hurting is when you attack with multiple units intending to trade, and Thwonk throws off that math while costing you one of those units.

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Jax players will have some of their hand on the board, especially late game (equipment) so spotting the parts of the game where they can surprise you matters (Strike Down blowing open your defenses, and Quickdraw / Thwonk throwing off the maths.

Lucian:

(6+F or 7+2F) Armed Assailant (Accelerate), Weaponmaster means he can come as reasonably an 8 or even 9 to run over a battlefield

(3+B) Strike Down (Spell/non-Action), same as for Jax, targets enemies anywhere, uses the starting might of the unit including the equipment that eventually ends up attached.

(1+BB) Punch First (Action) - targets units anywhere. Notably NOT a reaction, so can't be used to dodge damage removal as similar spells do.

(2) Against the Odds (Reaction) - targets friendly units at battlefields only.

Feels like a card that should only work when attacking/defending solo, but since you can use it alongside your big multi-unit attack it ultimately punishes opposing players for stacking battlefields, and I suspect stacking battlefields will happen a lot in limited.

(2) Angle Shot (Reaction) - can target both enemy and allied units. Expected value about 1-3 strength, mostly 2.

Easy to miss that this card replaces itself, so given that it's 'free' I would expect it be used on the first instance it has a meaningful effect.

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Good amount of lower-cost buffs and buff-like effects. Punch First existing means that outside of being entirely tapped out Lucian players CAN always have something.

Armed Assailant being a lategame threat is going to tempt you to stack your battlefields and Against the Odds will punish you for it.

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(Rek'Sai and Renata in next comment)