Do lures and incense actually work?

Lures seem to work better when there is a concentration of lured stops AND active players in the area. If you're a lone player and put a lure on a single stop, you'll probably get a small bump in spawns but nothing to get very excited about.

Incense, at least in my personal experience, is garbage. The only thing it has ever done for me is increase the number of trash mon that show up. But it works best (or really at all) if you're actively moving. I remember reading somewhere once that it results in a new spawn every x number of steps. If you start an incense and sit still, you're probably not going to see any benefit from it.

Not usually.
But with weather boost factored in it seem to work better.

I got a lot of lures and incense after buying boxes to get cheaper raid passes and incubators. Tested them last couple of days.
First day, normal boost, I got 4 Slakoths in lures/incense. Next day got psychic boost and I got 6 Ralts.

So it seem to work, but not really worth it without prolonged duration or really heavy investment.

I mostly get junk but did get a 96% lvl 30 Treecko from an Incense the other day, weather boosted.

I depend on incense if I want to catch anything at home (zero spawns) and get one mon per 5 minutes or so (6 total); I normally combine it with evolutions/lucky egg and it helps to evolve one more pidgey. But I don't only get commons.... rarer mon (one Snorlax in my driveway) and event mon also appear.

When I ride my Bicycle I get frequent spawns (every 200 meters I think) and catch them with the Go Plus. To me, it's worth it.

Lures spawns one pokemon every 3 minutes for 30 minutes. The quality of the spawns reportedly improves if there are more people playing in that area.

Incense spawns one pokemon every 5 minutes if you are sitting still. The number of spawns increases if you are moving, and if you are moving fast/far enough it will spawn as much as one pokemon per minute.