Well, since Microsoft has pretty much abandoned MS Reader… you might try using Calibre to convert the files to eOub or Mobi. That is, if there's no DRM on them.
As for your yes/no question — the answer is no, but allow me to additionally provide the reason.
The reason that there is no alternative LIT reader for Android and/or other operating systems is simple: writing a LIT reader would put the app developer in legally dangerous waters. LIT is a closed format created and owned by Microsoft and any attempts to support it would be quite questionable from legal point of view. Personally, I doubt anyone would want to test the abilities of Microsoft's legal department.
Quoting the http://en.wikipedia.org/wiki/Digital_Millennium_Copyright_Act to point to just one of many legal problems a developer might clash into:
DMCA "criminalizes production and dissemination of technology, devices, or services intended to circumvent measures (commonly known as digital rights management or DRM) that control access to copyrighted works. It also criminalizes the act of circumventing an access control, whether or not there is actual infringement of copyright itself." This is from the DMCA's wikipedia page
So, until Microsoft decides to officially make the closed LIT format available to the public, or at least modifies their relevant licensing accordingly… I wouldn't count on alternative LIT reader to be born.