SKYSEN Shed Door Lock Latch, Shed Door T Handle Lock, 5-1/2" Steam- 2 Keys- Shed Door Hardware- Black(Shed Lock-1)

I went with this one and have been happy with it. I have a similar build with doors about 3” thick. You need to install more towards the side of the door for the latch to work. SKYSEN Shed Door Lock Latch, Shed... https://www.amazon.com/dp/B0B3DGCJBX?ref=ppx_pop_mob_ap_share