1) I could not find my sock in the pile of laundry I did yesterday.
2) Please add this shirt to that pile of laundry which I will be doing later.
3) I have lost the pair to this sock. Sounds OK to me.
4) I have lost the other sock for this sock. A bit awkward but the sense is there.
If you are holding up the sock, then perhaps:
"I've lost the sock that goes with this (one)".
"I've lost the sock that matches this (one)".
not a teacher