Try coconut oil. She will likely lick it off,which is absolutely fine. They can/should get 2 teaspoons twice a day on their food.
It helps both ways: internally and externally.
Fish oil can benefial but it can also be harmul!
It depends on what your dogs diet is. Fish Oil is full of Omega 3 and Omega 6 fatty acids. There should and has to always be a balance between these two components! If they are out of balance health issues will occur.
If you feed your dog kibble with grain and plant oil which is both REALLY high in Omega 6 and then supplement fish oil on top of this he will likely be 'overdosed' on Omega 6 fatty acids. Either that or due to the heat processing all Omega fatty acids may be already destroyed. You just cant tell!
It also depends on what the protein source in your food was fed before slaughtering. Usually the protein source in kibble is fed a grain-hormone diet which,again, is high in Omega 6.
I would not recommend supplementing with fish oil until you know where you dogs food is coming from.
You can stick with the coconut oil for now,since you cant so anthing wrong with that if you only supplement 2 teaspoons twice a week or rub it on her lip