Hi, ! I think it's great that you are thinking of your client! I am not sure if her screen door can have a new door latch mechanism placed, but there are different locking mechanism options. One is a flip type lock that only requires one hand to flip the mechanism up or down. I will include a link to what I am describing, but please know that I am not recommending shopping from any vendor in particular.
https://www.amazon.com/Prime-Line-Products-155-Screen-Latch/dp/B006JFOYN4?source=ps-sl-shoppingads-lpcontext&ref_=fplfs&psc=1&smid=ATVPDKIKX0DER
Here's another version of a flip style lock -- https://www.google.com/shopping/product/1?hl=en&q=screen+door+locks&prds=epd:7982683374164907543,eto:7982683374164907543_0,pid:7982683374164907543&sa=X&ved=0ahUKEwik9pC-tev9AhVGj4kEHWj2DQUQ9pwGCAU
And here's yet another style of the flip lock -- https://www.acehardware.com/departments/hardware/door-hardware/door-latches/5573860?store=11296&gclid=CjwKCAjwiOCgBhAgEiwAjv5whFaOxaNBOtlG-SM6EOcBgCf9DS703mva_oiZZxKOsHIqKpgGeFphaxoCcCUQAvD_BwE&gclsrc=aw.ds.
This is the only type of lock that I have personally used and found to be very easy to manipulate, but perhaps other community members will have some suggestions as well.
I hope this helps!
Best, Erin, RheumatoidArthritis.net Team member.