I have an old-fashioned bleeding-heart ( Lamprocapnos spectabilis) that I planted quite a few years ago. It's blooming beautifully right now, late May. However, it's gradually being overwhelmed by lilies-of-the-valley, which are spreading and beginning to cover it. I'd like to collect some seeds from it this year and try planting them. Has anyone had any experience growing it successfully from seed ? If so, how did it turn out ?

I've always just dug up a plant and divided it as needed, on the spot, then stuck the divisions back into soil, even into late Spring. Their delicate and fragile looks will fool you - they are tough as nails.

I agree.
Also I did have volunteers from seed. Those were in the garden so if they needed stratification they got it naturally. I don't know if they require that.
I got wood poppies growing from seed in a pot by setting the prepared pot into the garden bed and letting the seeds fall in it, slightly stirring the potting mix to get them in just a bit. Then, natural winter weather cycle.

They can produce seed, but pretty sparingly. You'll have to look hard to find some if there are any. Related species have recalcitrant seed, meaning the seed can't dry out and should be planted immediately. (But they may not come up until next year.) I assume these would be the same.