If you still wanted to know, here is how you do it.
Reflect everything, or absorb it. Don't shield the gyro every time because it disappears, and then he can use another one immediately. Instead, spot dodge it, and then Fsmash it to make it yours, or reflect it (although this requires really good reaction time). If you Fsmash it on the ground it becomes a stage hazard in a sense, that it now yours. So it's basically if you had spawned the gyro yourself.
Also, R.O.B is one big hit box, which means Lucas can have a field day with him. The slightest opening on R.O.B's part should let you combo him to hell and back. you can easily get ~35% strings on him every time you get in.
Zair and PK Fire are pretty important too, since running up to him and just shielding doesn't always work. And since you have two decent spacing tools, why not use them? R.O.B will DEFINITELY use his.
Dair works well off stage, since R.O.B is so big. It's possible to just keep Dairing him and not letting him get back on stage. He can challenge you with Uair, but you can bait it out and stall with PSI magnet.
It's also pretty easy for Dthrow to Uair to connect since he's so big.
However, it's not a walk in the park: R.O.B is a character who can harass Lucas off stage (assuming you didn't tether) because of his good recovery. So try and tether if you can. He also out ranges Lucas up close, so be aware of that. Although he does get combo'd (?) easily, his weight means you'll have to put in a little extra work to get the kill.