I lived in a home with a cesspool for over 14 years and it was also built in the 1930's, maintenance is important in keeping it in good working order. You have the opinion of the Home Inspector and the opinion of a septic company that has been pumping the septic for years and states there have been no issues. Why not ask the seller to have a 3rd party septic company who can also certify it come out and give a 3rd opinion. The Inspectors job is to alert you to issues of concern, but they usually recommend that you have someone who specializes in that field do a further evaluation. Best of Luck.

From my own personal experience very similar to what you are describing (many, MANY moons ago) I would be EXTREMELY leery about a cesspool, especially lakefront. My biggest concern would be what happens if it fails? Most cesspools are grandfathered meaning everything is fine, until it fails. I don't know the area where you are buying but usually once a cesspool fails, it will need to be replaced by an expensive septic system. Lakefront that could be a real problem.
One way or another I would find out exactly what you are dealing with. And I would make sure that your contract has an a clause which allows you to withdraw your offer or get a price concession from the seller if major problems are found because you do not want to be left with the expense of a failed cesspool.

You can ask for the seller to ensure that the septic system passes inspection. Or you can get it inspected by an expert yourself and go with what your inspector says by adjusting the sales price of the home.

Terrence Charest, e-Pro