Ooh this is like my favorite MU and one of the easier ones to play as Lucas, granted you know how to deal with certain moves of Ivy...
Okay so Razor Leaf is actually very weak against Lucas. This is her main move to use in neutral & Lucas easily counters it: Dair, Fair, PKF, and run up -> shield -> punish OoS / shield grab, are all great tools against RL. Ivy's other tools to use should be spaced out Dtilt (decent end lag, bad at close range), jabs (close range, harder to punish, still bad on shield), and Fair/Nair. Her moves save for Nair (safe on shield & beats out PKF) all need to be max spaced, otherwise they're unsafe and easily punishable.
Watch out for getting grabbed / juggled. Lucas dies just as early as Ivy can in the MU. Her seed bomb (DownB) gets cancelled out completely by Dair, so they can't juggle with this unless it's an immediate use after a hit confirm. Fast fall Dair to go thru seed bomb then pick a safe landing option or punish her end lag.
Upsmash kills around 65-80%, so plan your combos accordingly to get her to about 50-65% then Dair -> upsmash. Fair -> Dacus works very well against her given the easy combo weight & angle it typically sends at. Most combos are easy to hit on Ivy.
Bair (according to 3.6) is smaller in range now by about 10-15% of the hitbox length, which makes ledge guarding Lucas harder. He can aim towards Ivy most times and usually trade with Bair or go thru her now. In 3.5 and previous, she could easily swat Lucas away. If you hard SDI it inwards & treat it like a Falcon Nair, you shouldn't have a problem escaping this ledge guard. Our local Ivy players JZ (PR) & Nom (previously PR'd) had difficulty ledge guarding me due to my great SDI on this move.
Everything else is pretty easy to escape of hers.
tl;dr Avoid Razor leaf and spaced out aerials. Try to kill her as early as possible (typically 75-100% stocks) to gain advantage over dying later (85-120). Respect her up close options of jab & Nair while not giving her enough space to Fair / Dtilt. Shielding isn't as bad in the MU, especially since she has a tether grab.