If you think they are outside, find out if any of your friends have a metal detector. Longshot, I know. You can also use a big magnet from a speaker, hang it from some twine and section your yard with it just above the grass. Hopefully it'll grab your keys.
But the odds are that they'll be underneath the big pile of siding you just created.
DON'T do the mowing until they turn up, I'll bet a mower would put a key-ring and keys into orbit. Or through your leg...