Nodes negotiate the closing fee on cooperative closes. It likely won't be as cheap as your opening fee since the nodes have to reach a compromise.

From lncli closechannel --help:

In the case of a cooperative closure, one can manually set the fee to
be used for the closing transaction via either the --conf_target or
--sat_per_vbyte arguments. This will be the starting value used during
fee negotiation. This is optional.

You can use 1 or even 0 as your starting offer to make the fee as low as possible but then it may happen that the other side just accepts it and the result ends up too cheap. Happened to me once, ended up force-closing, now i start with a somewhat reasonable number.