Thanks for the question: I totally understand what your friend is experiencing. Both me and my parents have went through this scenario.
I would treat the dog and the yard as two separate things:
1) I would apply DE to the dog as a deterrent for
fleas and ticks. I would also treat the dog's bedding, housing if it has a specific place that it sleeps. My lovely wife has written a quick guide to treating pets (and a lot of other things). You can read more
http://myabundantliving.com/diatomaceous-earth/
2) For the yard, you are correct that DE would work. It would not be my first choice just because it will also kill helpful insects and it is going to take a lot of DE. I highly recommend
chickens or guineas. We had lots and lots of ticks. Our 25
chickens cleaned up our 5 acre property in a short amount of time. My parents had massive amounts of
deer ticks and regular ticks. The
chickens cleaned house. This past year they added guineas will do the job even better, but they are noisy - very fun, but noisy.
Even if your friend cannot "keep" chickens, I would "rent" a chicken from someone. If he/she could keep 1 or 2 hens for even just a week or 2 in the back yard, not only would he/she have great entertainment, but they would not have ticks. They might have to rinse and repeat as needed. Obviously, the dog and neighbors could be issues, but there are creative ways to work around it.
Blessings!