A pun is a joke using words.. so the person is saying 'I am intending to make a joke'. It's a bit hard to explain, but in English we say 'Pun intended' or 'No pun intended' to kind of make things more funny. I think the joke here is that the company sell lunches, and they are saying their competition will eat them for lunch if they don't look after their customers. 'Eat them for lunch' here means 'take away their customers (their business)'.