Doing a short hop dair into FP on the edge is brutal especially against big characters. If you notice people are always correctly DIing away on the fair, just shoot a small AS for that possible extra damage and off stage zoning. You want to hit the fair very close after the jump so you do a rising fair. Another option is first hit of down air into FP. This is decently Diable, but should work on big characters. Upsmash ->FP can work if they hold up and in, but there are almost always better combos unless near the ledge especially with ACSing. If you don't know, Lucario's U throw and D throw are DI mix ups (good DI for one is bad for the other, and vise versa). So you grab someone near the ledge with you back facing the ledge (most often with edge guards), they will often hold toward the center of the stage, to DI for the Dthrow to not get comboed, Bthrow to not go as far off the stage, and holding in for survival DI. This means you can get an easy Uthrow into the powered FP which is guaranteed on almost every character ( even most floaties like mario) and we know this move kills at like 40%. And of course if they catch on, just mix up with some Dthrows, and get a meaty lucario combo.
Don't forget how powerful the powered version of the grounded version is as well. I find many Lucario players neglecting this move even though you can essentially get a kill of a grab(like on shield) at around 85%.