No they are different. Laceweight in the British system is usually described as a 2-ply (a 1-ply is a thin lace, perhaps a cobwebweight). 4-ply is thicker and is equal to sock-weight (3-ply could be called a thin sock-weight).
However you could double-strand the laceweight and I imagine get something close to fingering (snigger - sorry, I think that's a hilarious word for it). You would have to swatch to be sure. I think it would be easier though to go with sockweight/4-ply.