Under Settings, Options, Tax Return, Tax Return Options, change Computer Date as PIN Signature Date to No. You don't need a date to e-file an extension; without a manually-entered signature date the return won't e-file. You'll want to change that for all your modules.

There's no e-file rule that says an entity return with no revenue isn't e-fileable; my guess is that if you look at Forms, the balance sheet will be blank (because Lacerte thinks it wasn't required) so being out of balance isn't an issue, either.