Of course you can try the low light. Doesn't mean it will stop them from turning on the overhead though.
Have they always had all those lights in their room? Nightlight, dreamlight (whatever that is... I really am not sure), etc.
If you are okay with the other lights, I am not sure what the big deal is about the overhead, unless it is a ceiling fan that has half a dozen bulbs and is runs up the electric usage or something. Then just go with a lamp, and just tell them, it is the lamp only.
Have you asked the 3 yr old why he has been doing it? That might help you decide how you want to handle it (or whether to ignore it). Is he potty trained? Does he want more light in case he needs to get up and go to the bathroom during the night? Has he had a scary dream recently? Seen something spooky in a movie that happens in the dark?
My son used to like me to leave the light in the hall on (I would pull his door partway closed so the light wasn't glaring into his room though. Then I would just go turn it off after he fell asleep. Eventually I started delaying turning it on, or I'd come turn it off before he was fully asleep. And it became a thing of the past.
My daughter has never wanted any kind of light (and we never had nightlights in their rooms, even as infants). In fact, she asks me to turn off lights in the family room sometimes, if they are shining too much light into her room at bedtime.