Sun room lockset needed

I?m having a tough time trying to figure out the correct lockset needed for my sun room lanai. The door thickness is 2 3/4. The offset from for edge to center hole is 1 1/2. At the door striker on swinging door the center holes is 8 1/4 and the overall square cut out is 7 1/4. I believe the last homeowner rigged another handle when the original broke. See photos and hopefully you have something that will work or lead me in the right direction. I did talk to someone a while back at another business and was told a mortise lockset is what looks to be the style. I do not have the original lock nor do I know the manufacture of the sun room. Thank you.