Help needed with lizard identification

"Picking it up & putting in outside would not solve the issue."

Sure it would. It would be out of your bedroom and out of the house which is what you desire.
See if you can coach it on to the end of a broom and RELOCATE!
Or take all the screens off your windows and herd it to the openings, the replace the screens.
Come on, it's just a lizard, I am sure you can outwit it.

I woke up Christmas morning with a rather large brown recluse on the ceiling over my bed and head.
Not my ideal morning surprise and as you may understand with the adrenalin pumping thru me, there was no need for morning coffee or tea, except to relax. The vacuum worked quite well in this instance. Glad the day improved dramatically after that.