If it helps, you can click and drag the vlookup from cell to cell, so you could populate A1 with row 1, then drag it across. Use '$' symbols on anything you don't want to change when you drag.
So, if your lookup was:
=vlookup(A1,othersheet!A:F,1,FALSE)
you could change it to:
=vlookup(A$1,othersheet!$A:$F,1,FALSE)
and it would still work as you move it around