Stickers on Painted Wood

I would be nervous about putting lacquer over the stickers for fear of damaging them.

Test with one sticker on some scrap that has been treated similarly to the bike/rocking horse.

One alternative might be that decoupage coating – I believe it’s water based.

But – as always – test on scrap first.

-- Bob www.singularengineering.com - A sideline, not how I earn a living

You will really want to test before you put anything over the stickers, but I would put something over them.
I would also finish over the spray paint as well. Stuff for kids takes a bit of a beating, and any added durability will be helpful.

If you can replace the stickers with decals – then use decal set. This stuff dissolves the plastic decals and sets the paint part of the decal. When I had trains – many many moon ago – I did this and lacquered over the work. Looked like it was hand painted.

-- David in Damascus, MD