No. BBeB (LRF and LRX files) is Sony's propriety format so only Sony devices support it. I don't think FBReader developers have any plans to support LRF either.
Conversion of LRF to ePub or Mobi is simple in Calibre and both these formats can be read on the DR1000. If you consider this too much of a hassle then a Sony PRS is the device for you.