On this type of latch (mortise) the third screw is often stripped (because it’s a set screw that holds the lock cylinder in place and often the notch in the cylinder is misaligned / on the wrong side) but _un_screwing it should be easy.
The cylinder itself, however, is usually finely threaded and can require a fair amount of torque to get started, especially without using the key for additional purchase.
Ah a fellow haberdasher #tips-lady-fedora