Oh this discussion will be productive ;D
I love the fact this is the MU since it is my favorite two characters (<3333). So I think I can go at this from both sides and can be unbiased to either character.
Alright ima explain the MU before I give a ratio. Hope you like ;]
Okay so let me break this down a bit.
Piece Game:
Let's start with the piece game since that is how the battle starts. ZSS should try and keep one piece on the stage against Lucas to do the most damage. She of course wins the piece game and should know how to handle her pieces however Lucas can be annoying with them if the player knows how to use pieces (like myself but lol i don't count). ZSS can pick up pieces better but both can keep them alive. Lucas should most likely just dispose the pieces while ZSS should keep one. ZSS wins this one pretty obviously.
Ground Game:
Lucas has better smashes than Zero Suit Samus. His early killing powerful smashes can kill ZSS kindof easier than harder. Fsmash is a quick smash, and well timed Downsmash on landings or a Usmash from ZSS's air approaches could mean trouble. Plus all of Lucas' moves can be extended on stages like Brinstar, Green Greens, CS(phase two) which is even worse for her. However ZSS has better kill set ups with her Dsmash (which has really great range <3). Plus most of ZSS's moves get us into the air which means trouble for Lucas since ZSS has the superior air game. But Dsmash can be PSI Magneted which heals about 28-30% of damage for Lucas and the Paralyzer can also be Magneted being 10-14%. So using Dsmash and going crazy with it isn't the best idea here at all. (*quick note* Lucas heals more than Ness so it is worse for you to use it here than against Ness [<3 Lucas])
Air Game:
Anyways lol getting off topic. Back to Air game. Now in the Air ZSS is the obvious winner. Uair when spaced right beats even our Dair. ZSS, however, outpriotizes our air game alot. Lucas should be sticking to the ground while ZSS should be trying to get him in the air, but ZSS should not forget Lucas has above average air mobility.
Camp Game:
Now camping time. Lucas has the better tools to camp ZSS with his projectiles however her Side-B is a very annoying pressure/spacer on Lucas but Lucas's Side B has more range than her Side-B (iirc and wtf lol). Anyways it is Bad for Lucas to be camping ZSS though because PS > Dash attack is annoying for him. Lucas should be trying to get as close as possible to ZSS. Lucas wins in camping terms. (however it is preferred he doesn't).
Grab Game:
Grabby Grab time, Lucas wins lol. ZSS has the worst or second worse (the only grab I would say is worse is Yoshi's). Lucas needs to remember sheilding is ZSS's bane. She literally has no grab game to speak of. However her grab moves are pretty decent if she lands it, if she doesn't land the grab....im sorry but ZSS will be eating a Usmash. (it is really painful for her ;[) Lucas has the better grab even though it is a tether grab as well. (however which grab game isn't better than hers? it is pretty terribad.) Lucky for ZSS there is no Dthrow->Utilt for us but Dthrow is a kill throw plus he can still throw you offstage where ZSS is not at her best. So near higher percentages ZSS should try not getting grabbed by Lucas since she is light.
Gimp Game:
Now this next one is weird, Lucas has the tools to be a ***** to ZSS offstage and if ZSS follows Lucas to try and gimp him she might not be making it back (it's upsetting). Lucas has the better recovery since he has a tether, Zap Jump, WaveBounce, and PKT2. However ZSS can do a bit to mess with his recovery. ZSS can Dsmash his PKT2 and possibly get the Spike (O___O) *this is iirc* and to annoy his recovery via Wavebounce and Zampjump she can Usmash or UpB to annoy us (however neither is like a kill or really dangerous, just annoying.) And Lucas needs to not be predictable with his Tether or ZSS can predict it and get a Dsmash on us *NOT FUN AT ALL!*. If Lucas tries to edgehog ZSS here is a few things she can do 1.) if she is under the stage she can actually drag Lucas down with her (lol i pulled this off a few times with her. Seeing peoples faces are priceless xD) 2.) Flipstool us 3.) Spike us via DownB (if our invincibility is gone) Plus she has a very good improved jumps. Jump+UpB = 33% better jump (right? gah I suck at remembering x-x) Edgehogging is not the best idea for either character. Lucas can gimp her a bit with PKT however she can DI it and get a free ride back to the stage, but both PKT and PKF are annoying if he can predict her Third Jump (a.k.a. DownB). I wanna give gimping to Lucas but it is kindof a draw imho. ZSS isn't the easiest person to gimp especially a good one. However I don't think ZSS should be gimping a good Lucas anytime unless he is recovering below. Basically both characters need to be really unpredicitble to not be gimped. Good ZSS grab that edge FAST especially with the range on that Side-B and UpB range+Jump from below WHILE still having a backup third jump that can spike.
tl;dr
ZSS>Lucas Piece Game (well ZSS should have better control over her pieces xD)
Lucas>ZSS Ground game
ZSS>Lucas Kill Set ups
ZSS>Lucas Air game
Lucas>ZSS Camp Game (not recommended for either though ;S)
Lucas>ZSS Grab game (....lol this is an obvious one)
Lucas=ZSS Gimp game (this is weird lol anyone gets it it's Lucas but eeeeeeeeeeeeh someone else talk about that xD)
In the end my conclusion is this MU is even as heck. However each character has a chance to make the MU in their favor based on stages. Otherwise it is a pretty nice stalemate (btw FUUUUUUUN MU to play if both sides knows this).
50:50 or 55:45 for either stage dependant. Really it is close these two.
Silly randomness: Lucas/ZSS make a good combo since they handle most of each others MUs and in teams omg I looooooove this team. it is really good.
Okay I hoped this was productive/helpful and stages are gonna be weird because some stages ZSS will win the MU by a bit and others Lucas wins on. Lucas should be banning Lylat and RC and maybe Norfair if it is Legal. While ZSS should be banning Brinstar (even though she does well on here Lucas is **** here), FO and maybe JJ. Also ZSS should try and not go to stages that extend Hitboxes. It hurts her more than helps. ZSS should be picking stages that get them to fight in the air the entire match. (i.e. RC, Norfair, Lylat) RC, Norfair and Lylat make the MU in her favor. Lucas gets his solid 55:45 however with Brinstar, Frigate (because of the edges for poor ZSS ;( ) and Jungle Japes is just bad for her, like really bad. The bad thing about ZSS's really good stages for Lucas is that Lucas doesn't do horrid on those really (besides Lylat which I hate with a passion). Also taking Lucas to either Smashville or Final Destination is not good for ZSS but it is good for ZSS to try and take him to Lylat, Battlefield, and uhm YI but that stage is pretty terridbad for both of them. (lol who gets to strike that stage first xD) Oh PS1 is good for both but ZSS does better on it. (I like PS2 for both =P) Lucas does well on Battlefield don't get me wrong but against ZSS it isn't good for him at all.
Stages tl;dr
Lucas Stage strike, cp, ban:
Strike: Yoshi's Island, Lylat Cruise, Battlefield
CP: Brinstar, Frigate Orpheon, Jungle Japes (<---try for JJ if it's legal)
Ban: Rainbow Cruise, Lylat Cruise, Norfair (anything with CRUISE in the name lol)
Zero Suit Samus Stage strike, cp, ban:
Strike: Smashville, Final Desintation, Yoshi's Island
CP: Rainbow Cruise, Lylat Cruise, Norfair
Ban: Brinstar Frigate Orpheon, Jungle Japes (!!! This one if it's legal)
BTW since both characters are a rare breed this MU is rarely played =P. (still fun/close)