As you can see from the
E-book Reader Matrix, the LIT format isn't usually supported. Only the Hanlin's include this and in the UK the BeBook One appears to have been discontinued. There may be other sources of a Hanlin V3+, since they are sold under many names. Even on the Hanlin's, support for LIT has been hit and miss.
I think you are better off converting to ePub, or (for the Kindles) MOBI, using Calibre. Then your choice isn't limited by format. If you want a device with wide format support, then the BeBook Club or Neo are one option. Another is Pocketbook, and note that the 602 is out now but not in the Matrix.