Placing a cookie sheet under my pyrex baking dish in a convection oven
Yes.

The instructions with my oven say to always leave the grill pan/roasting dish [which is of course the full size of the oven area] on the bottom shelf rungs, even if you're not using it for any other purpose, simply to catch spills.
A cookie tray would certainly serve a similar purpose.

Assuming you will pre-heat the oven, then it will all heat up at the same time, before your lasagne goes in, so won't change your cooking times at all.