How long should Lamb leg steaks be cooked for? Is there a rule of thumb for the weight or cut? 

I'd prefer to err on the side of well-done, as I want to serve it to my toddler.
Treat it like beef steak. Super-hot pan, slap it on, keep pressing it with your finger, when it feels very firm, it's well done; about 5-6 minutes a side in general but it will depend on thickness; the finger test never lies. Let it rest for a few minutes after cooking.