I would suggest if you took the broken string to a good music store they should have a string gauge tool to match it, or gauge to string near it. Otherwise just in general .010 should do for the shorter strings. You can try to tie off the string looking at how he does it or just use the ball end on the rail pin works just as well.
Thank you for responding. I put a caliper on the string and it read 12, but that seems heavy. I will visit a stringed instrument store, as you suggested, and see what they can tell me.
Dave Lucas does tend towards a little thicker gauge string than I use personally on my Dave's Psaltery.