Door latch replacement

I am afraid your old Sears Storm Door Handle Set isn't made anymore but we do carry a few options that customers with Sears hardware have been able to use as a substitute. See the 40-131 lever handle set with a deadbolt. This is similar to yours but without a key cylinder to unlock it from the outside. If you want key access, you would need to install the 40-058 lever handle with a deadbolt.

Now, your door is fairly thick for a storm door but these would still be our best replacement options. Keep in mind that you may need to pack out the handles with washers to accommodate that size. Take a look and see what you think.