I feel you on the lag it's hard to play fast fallers unless you have a really good connection that's why I just gave up on the one match I tried to play Wolf lol. As for Marth's throws you always want to DI away from him.
Edit: General tips: Learn to wave dash, rolling sucks and will get you punished. Don't spot-dodge so much, it's easy to bait that goes back to my first point about wave dashing, evasion is always superior to defense.
Character specific:
Lucas: Don't shield grab so much, Lucas' grab is really laggy when you whiff, also try to mix up your recovery a little more you kept recovering the same way against my Marth and you were just setting yourself up for those dtilts, and don't charge up when you respawn because you're basically just giving up stage control.
Peach: You rely way too heavily on turnips, they're good for zoning, and escaping pressure with glide tosses, but that's about it. Also be conservative with dsmash it's really punishable. You should work on float cancel combos because they can apply ridiculous pressure. Also learn the timing for her DACUS, and try to incorporate footstools into your gameplay because she has some pretty sick footstool combos.