I wouldn't. I have a valentini who eats anything remotely looking like a shrimp, so I'd imagine a lobster would get eaten right away. It's pretty normal behaviour for a puffer.
Mine wouldn't touch live shrimp for months and would only accept flake foods, he wouldn't even eat frozen mysis. My snowflake eel eventually ate all the feeder shrimp I added. A few months later I decided to try feeder shrimp for the puffer again and he went crazy. It was like an instant rush of excitement and ate 3 large shrimp about 2/3 his body length in a matter of hours. Now I can't add anything but fish to the tank lol.
So even if you do add the lobster and it goes in unharmed, expect to have him go missing eventually.