When eating lobster, what is the green stuff that is often encountered, and should it be eaten? How about the red stuff?

The green stuff is the lobster's liver or more accurately, its digestive system. Although many people like to eat the "tomalley" it probably isn't a good idea because this is where pollution in the lobster's own meal choices would become concentrated in the lobster's body.

The red stuff is the roe, the unfertilized eggs of the female. Lobster eggs were once considered a delicacy, like caviar. The roe is also called "coral" because of its bright red color.

https://www.allrecipes.com/article/green-stuff-in-lobster/

https://lobsteranywhere.com/seafood-savvy/lobster-lingo/

Lobster

Issue: Should I eat the green stuff? How about the red?

Solution: That depends on how squeamish you are. The green mass, called the "tomalley" serves as a liver and pancreas, and thus absorbs toxins. It is, however, considered a delicacy by many lobster lovers. Use your own judgment, pay attention to local advisories, and limit your consumption to no more than one lobster's worth per day. As for the red stuff -- if you've encountered any, you've hit the crustacean jackpot. It's unfertilized eggs called "roe" or "coral" and is a taste treat on par with caviar.

http://offshorelobster.org/main/lobster-facts