Unlocking Lynx : Taming.io (Method in description) 

I noticed that I had a decent amount of tames on lynx so, I decided to grind tames on it for a few days. The method used is very efficient for common pets. (I was grinding for like 3 days)
Step 1: Spawn about a 1:30 before your pet's biome
Step 2: Kill animals until 2.5k gold
Step 3: Buy Tamers cap
Step 4: Run around the map looking for your pet and tame it
This method lets me get around 1 tame per 5 minutes.