How can one replace a Lori branded lock that won't fit in a new door
I had a lot of trouble finding information on this lock and I'm pretty sure this style is not as common as I've never encountered it before. When I realized that my key for it was a Kwikset keyway, I determined that it is the same keyway used on the user rekeyable smartkey locks so I ordered a Kwikset 980 (~$25) and was able to re-key it to the Lori key.
Your results may vary
I called Kwikset support to ask if I'd be able to use a non-kwikset key (although it is a Kwikset KW1 keyway) on the smart lock. I was told it may or may not work and they guy had never heard of Lori locks.
In this case, I'm happy it worked.