I have my LTC in mass. And live near the NH border. Can I buy ammo at the walmart in NH or would I need a licence in
NH to be able to buy it there?

Does Mass have any laws about 'Transporting Ammunition Across State Lines"?
While they are required to check AGE, I don't believe one needs to show DL to prove residency. (but I could be mistaken)

Of course... You could Call the NH WM and ASK.

You're fine in NH, as well as ME (I buy at Kittery Trading Post all the time). The only place in New England you'll have a problem is CT, but you can get an out of state pistol permit from them and buy there.