For one, you roll too much. Spacing yourself is great, but rolling is going to get you killed. Try and run away instead. Also, put B-sticking on. You can spam as much PK Fire with that on keeping you at a farther distance between you and Marth because the PK Fire will push you back, but also fire off from where you started it. If you don't know what B-sticking is, it's simple. Just change the controller setting on your C-stick which are set to "smash" attacks and change it into "special" attacks. Your C-stick will now use what your B button would normally have. Once you have that set, save it. If you walk to the right, jump and hold right but tilt the C-stick to the left, you'll fire PK Fire and bounce back and vise versa. You should anyway.
Here is what you'll get out of it.
http://www.youtube.com/watch?v=Kox5-m5JM3w
You may be called a spammer, but the point is is that it's good for spacing so you don't get hit by Marth's sword and you'll also be able to launch an annoying attack that can pressure your bother's shield. Don't rely on only this, though. Also, as pointed out, you use down smash a lot. It's good if your opponent is rolling around you, but it's not good to use if your opponent is jumping. Avoid using Lucas' up smash all the time, too. You kept that at a minimum which is good. Another thing is is that you look like you're afraid of approaching your brother. You really shouldn't have to approach Marth, but if you do, don't hold back using whatever you need just to injure Marth.
If you use your nair, which is outrageous and Marth uses his fair, there is a possibility of you hitting Marth anyway, though he still got you. Lucas' nair is really good at pressuring shields and useful against spot dodgers. Lucas' fair is pretty good, too, but I'm not so sure if it's good enough to break through Marth's fair. Also, you use PKT2 quite often. If you use your PK Thunder, be sure to keep at a distance when you use this because I saw Marth would hit you quite a lot whenever you did this.
Spacing is key and knowing your opponent is also another thing. You're bound to get hit, yes, but still, try to keep yourself from getting hit. Again, don't be afraid to spam PK Fire. You can also search on YouTube for some good Lucas mains to see if you can improve your play style.