Lockable inside Latch for 40-034?

A handy person from Seattle says:
Can you confirm that this door handle set has a lockable inside latch? I know it is not a keyed door handle, but I want to make sure it can be locked from the inside. Thanks!
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Tom from SWISCO responded:
There is a lock on the inside latch of the 40-034.
A handy person from Seattle, WA says:
Thanks for the quick reply. So, is the Sears Storm Door Handle Set (40-043) the only one with the lock on the inside latch? Or, does the Keyed Handle Set (40-034K) have a lock on the inside latch in addition to being able to lock it with a key?

I currently have a keyed handle set similar to the 40-034K but don't really need a key, just an inside lock, if that is possible. The inside latch for the Sears handle set (40-043) that is shown in the photo looks very much like the one that I need to replace, but my storm door is 1-1/4" thick, and the handle looks nothing like that.

Rather than replace just the broken inside latch, I would like to replace the entire door handle set with something similar to what I have. Thanks!

A customer submitted photo of a door handle.
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Tom from SWISCO responded:
I apologize for the previous typo; I meant to type 40-034, in reference to the Out-Swinging Door Handle Set, which appears to be what you're looking for, not the 40-043 Sears Storm Door Handle.

The 40-034K also has a lock on the inside latch.
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