Did Gimli lie to Eomer?

A little thread necromancy:

Christopher concludes it was indeed a slip, I think due to some shuffling of the drafts, though I can't check, not being near my library.

I believe the prolongation of the company's march through Lothlorien was responsible for a similar contradiction, when Aragorn says "But tonight I shall sleep without fear for the first time since I left Rivendell", even though the previous night they had "rested and slept without fear upon the ground".