I'll try and answer each one of your questions.
Lucas' primary approach option will most likely involve SH PK Freeze or SH DJC PK Freeze. Shield it. If it fails, Lucas will most likely retreat and keep trying. All other approaches require Lucas to be next to you. I would be ready to do a retreating aerial. Be ready to punish!
All of Lucas' moves combo. Not very helpful, and I can't even really describe how to DI. This is definitely a "don't get hit" type of matchup.
I can't really comment on Lucas' weakest area. But most players will become very impatient and want to just approach you, even if it is a mindless approach. Punish their aggression! Fortunately, all of your characters seem very suited for this.
His best KO move is OU up smash and back air.
Lucas doesn't really have a "best" OOS option. Expect him to use a rolling option or jump out of shield to aerial or even magnet. That being said, neutral air out of shield is common as it hits on all parts of Lucas.
Lucas has amazing shield pressure. I would recommend just rolling away. Lucas is indeed susceptible to shield pressure.
Not many aerials in the game are safe on shield at all, if any. That being said, Lucas' fair is -1/±0. Bair is -2. Uair is -1. Dair is -5. Nair is -5. In a realistic situation, however, Lucas' aerials are safe coupled with magnet which people will usually use afterwards similar to spacie pressure.
Lucas' threatening throws are up throw and down throw. Back throw can kill you if you are tricked into DI-ing it improperly. DI directly left or right to properly DI up throw. Down throw puts you behind Lucas so DI behind Lucas. Be wary, however. Lucas can DACUS quite a few characters out of down throw even if properly DI'd. If you don't DI, Lucas can up smash or start a combo string, most likely with down air.
Regarding chain grabs, Marth can fthrow Lucas multiple times and end with a tipper if improperly DI'd by the player. Meta Knight has down throw, of course. Snake has his up throw.
When edgeguarding Lucas, it can really depend on your character and playstyle. I play Meta Knight primarily, so I have the liberty of having a good recovery with multiple jumps. This means I can go ahead and risk using the last hit of forward air offstage to edgeguard, as well as back air walls. When Lucas tethers and you are on the stage, there can be some situations where you can actually decapitate Lucas as his head can pop up from the ledge. Use down tilt to achieve this, especially with Meta Knight and Marth. If Lucas tethers the ledge and you are edge hogging, be careful because Lucas can tether drop and magnet you into a terrible position offstage, or up special to kick you off and recover simultaneously.
When Lucas is edge guarding you, it will almost always come in the form of back air or down air. Be extremely aware if Lucas is moving towards you while you're recovering! Lucas' sweet spotted back air is a spike and will kill you. Even the non-spike angle on it is deadly. Down air is also a menace to your recovery. It may just be my preference, but whenever I play Lucas I'm willing to trade my down air with my opponent's recovery. The first couple hits of down air lock you into the combo, and then the final hit meteors you. If you can react fast enough, a meteor cancel is possible off of the last hit and quite possibly save you.
Out of all your characters, I think Mewtwo would be your best bet. Mewtwo is great at keeping opponents off of the stage with back air walls, and a typical Lucas player will always try to tether. This put them in the range of your tail, or even a falling neutral air to drag them down (risky on small stages.)
If you need anything else, feel free to ask. Otherwise, good luck at Zenith.
