Something like the CO2 Wash process could be used to upgrade this gas to pipeline quality.

It is somewhat ironic that the methane in the lake comes at least partially from farm runoff.  Eliminating this input would cause the methane to be renewed more slowly or not at all.  To make this resource totally sustainable would require that the watershed keep putting excess nutrients into the lake — nutrients which could be at least partly produced from the methane itself (reform to hydrogen, convert to ammonia via the Haber process).

I have to admit, I find this little twist amusing.

Sounds like Cradle to Cradle agriculture :-)