They wouldn't fit the singer because they don't have a flat side they're rounded and then they have a groove at the side same as the chain stitch needle has but they're about 4/5 mm longer so that in the chain stitch machine the presser foot couldn't be used. The guy said you could cut them down but seems a shame since they're vintage some of them look a little squiffy as if they've had rust removed or something... There's sort of a texture along the groove so they might not all be viable ...I assume the lockstitch has the same pin as the chain and that might get damaged so someone might want to check each one carefully.
I think I have a few of the old singer treadle needles which seem to have a needle length groove but a flat edge at the top where it slots in. They seem quite long. I haven't cleaned the treadle one or oiled it yet. So can't really check but I think it will be easy enough to find singer needles for it.
Did I mention the sock knitting machine we also found! Didn't even know such a thing existed!! 😃 I might go over to my aunts and have a fiddle with the treadle for some fun for the evening!