I have recently obtained the following bottles:

1955 Chateau Lanessan Medoc
1966 Chateau Ripeau St. Emilion
1971 Chateau Beausejour St Emilion

I am interested in finding out a bit more about them, including if they have any sale value. Anyone have a suggestion on where to look?

1971 was a good year
1966 was a good year
1955 was a very good year

If your wines have been stored properly, your wines would be worth approx:

1955 Lanessan - $100-200USD per bottle
1966 Ripeau - $50-100
1971 Beausejour - $50-100

Unless you can prove these wines were stored in a temp/humidity controlled cellar, they would likely be worthless vinegar at this point and finding a buyer would be almost impossible.

I would personally drink them. These are not highly demanded chateau from top years, so why sell them?

These wines are probably well past their prime. Drink up

I just had a '66 Ripeau over the weekend and I am sad to report the name should just be RIP. The wine was stored properly, but was too far gone.

So, I can only assume that my recently purchased bottle of 1970 Chateau Beausejour has tanked as well?

Not necessarily. It should certainly have a longer life than the 1971. With ideal provenance, it could be fine. I'd guess it's declining by now, but don't give up on it. Open it at your earliest convenience. Good luck and have a backup handy.