So after finishing my 1,000 lapras encounters my data says that you get 3.3 lapras enoucnters per expert lure. So in order to get 27,000 lapras encounters you would need to use about 8,175 expert lures. I would have loved to get the encounter rate data but unfortunately this game still has not added a simple encounter counter.
I was also able to confirm that using only balls that it is about a 28-29% encounter rate to catch lapras.
Below is the formulas I used for my data table incase someone was wondering where I got my calculations from: