There are some good organic fertilizers which will do the trick.
Blood meal is the dried blood left over in the production of beef.
Sounds gross, but it is a wonderful lawn fertilizer. Make sure to water well after application. Blood meal can be a little pricey, so perhaps you'd prefer Chicken manure. It is widely available and a terrific organic lawn fertilizer. To minimize the damage done by dog urine, try spreading agricultural gypsum over your entire lawn, twice a year.