I have a lot of experience in this MU via practicing with my friend who mains Lucas and Roy.
I firmly feel Link wins this matchup, but you have to really play a certain way and stick to it the entire time.
Neutral Game: At first glance, Lucas' neutral is terrifying against Link. Nair racks up easy damage and leads to strings if you slip and get hit by it, and PK Fire keeps you at bay constantly. Couple that with Lucas' Zair, and it feels like Lucas dominates the field.
The best thing you can do is concede the stage to Lucas and take advantage of his zoning with your own. PK Fire can eat Boomerang, I believe, so angling those upward to catch Lucas mid-air is key. Bombs are extremely helpful here, as they usually blow up on his Zair and damage him. Arrows are good when Lucas is using his PK Fire a bit too much. Pay attention and heed his Zair though, because, as I said it eats boomerang and sometimes a full hop Zair can pass by Lucas.
Of course, you need to approach eventually. What I do is after landing a boomerang or bomb, I immediately move in to capitalize on Lucas' lacking landing options. That said, you obviously want to play mid-range, in order to have a chance at actually punishing.
Fair is a really good move in this MU. It does big damage, is pretty safe with it's range and overall is a big problem for Lucas. Bair is good if Lucas ever tries to get in close, you can sh Nair pretty easily or sometimes landing Nair to punish if he's below you.
CQC/Close Range: Neither Link nor Lucas are especially comfortable in close range, and I feel Lucas suffers more in this area. His close range options are jab, grab, nair, and sometimes sh fair. You want to space your nair and fair here to beat out his aerials, be sure to space them well because if not you'll take the hit and Lucas really wants the momentum from getting those hits.
Lucas' jab is annoying, but he doesn't get too much off of it. You want to try and beat his out with yours, and at high percents you can even kill with jab2>up b
Avoid getting grabbed at all costs. Lucas' grab is a big deal, since Link is so heavy, he can usually get two or even three Nairs off one at low percents. He also gets up air and sometimes fair from down throw, so what I recommend when getting grabbed is to not panic. Lucas needs a read for up air, usually, and if you DI right you can avoid more nairs after the first. If he doesn't nair immediately after his dthrow, he's trying to get a read for up air. He either needs you to DI left or right, here all you can do is learn your opponent and try to counter what they tend to go for.
When/If Lucas tries to approach, he will often use Nair, Zair, or grab. Grab simply requires not being hit, and you can obviously punish it a plethora of ways, since it's a tether grab. Nair will often move onto your shield then move out in an attempt to avoid punish, but you can easily grab or jab.
I don't recommend using many smash attacks at all in this MU. Lucas will easily punish any missed smash. The safest one is upsmash, if he's on a platform above you, but don't rely on it because Lucas can and probably will drop platform and fair you in the face.
Landing is difficult for both of us, though Link is easier in this match. Lucas can either opt for dair or nair and hope you grab the wrong direction, or just go for ledge. You should be able to catch his ledge attempt with a boomerang or fair. If you have to land, use bombs to cover your landing. His up air will blow up the bomb and get him off your back.
I'm not sure I've said all I want to say but I hope this helps regardless
