LPFM stations are not required to maintain a public file similar to those required by full-power stations. (See §73.801 for lack of reference to §73.3527)
LPFM stations are required to maintain a political file. (see §73.801, §73.1943)
LPFM stations are not required to allow for public inspection of their political file and with the recent introduction of online public files, LPFM stations will not be granted access to the FCC's Online Public File system for uploading documents. (REC inquiry with Staff, 2/1/2016)
LPFM stations are also required to maintain station logs indicating when the transmitter is turned on and off, variances in operation and the extinguishing and replacement of any required lighting of a commonly-owned tower. (see §73.877)
LPFM stations are also required to keep EAS logs. (see EAS Handbook)
Despite there being no LPFM public file requirement, REC encourages LPFM stations to voluntarily make a public file and put it on line in the Voluntary Public Inspection File system. https://lpfm.ws