I'd suggest you set up a memorial on www.findagrave.com
using what info you have, and then ask for a photo of her headstone. It's free, but you need to register.
There are already some Lucyshyns on findagrave:http://www.findagrave.com/cgi-bin/fg.cgi?page=gsr&GSfn=&...
If any of these are her children, they can be linked to her memorial after you set it up. You can also request them to be transferred to you.
You should also check your alternate spellings for other relatives on findagrave.