IAAF rule 170.6 says
The baton shall be carried by hand throughout the race. Athletes are not permitted to wear gloves or to place material (other than those permitted by Rule 144.2(f)) or substances on their hands in order to obtain a better grip of the baton. If dropped, it shall be recovered by the athlete who dropped it. He may leave his lane to retrieve the baton provided that, by doing so, he does not lessen the distance to be covered. In addition, where the baton is dropped in such a way that it moves sideways or forward in the direction of running (including beyond the finish line), the athlete who dropped it, after retrieving it,
must return at least to the point where it was last in his hand, before continuing in the race. Provided these procedures are adopted where applicable and no other athlete is impeded, dropping the baton shall not result in disqualification. If an athlete does not follow this Rule, his team shall be disqualified.
There's nothing in there that says you can't wait till the next lap to pick up the baton. There's not even anything in rule 170 (the rule for relays) that says the lap wouldn't count, or that the baton has to complete all laps. You just have to pick up the baton and return to where you dropped it if it rolled.
That returning to where you dropped it part would ruin everything, because you'd still have to stop and turn around. Otherwise you could try to scoop it up without stopping.
It surprises me that there's nothing in there saying the baton has to go the full distance. It just has to make every exchange legally. I suppose you could take the baton, set it down carefully in lane 3, then run 3 laps and pick it up again. It would be stupid, but legal.