Even in Belarus itself, the base for a "LitBel" union was very weak. In OTL, a merge between Lithuanian and Belarusian Soviet Republics was pretty much forced by the Bolsheviks because they couldn't decide which side gets Vilnius.
As for your scenario, well, one of a number of problems is that there is no plausible way for the Bolsheviks to take control of all of Lithuania while losing Belarus at the same time. Belarus was pretty much in the middle of the Polish-Lithuanian-Soviet front, and if the Bolsheviks lose Belarus, the only way for them to supply their forces in Lithuania would be through Latvia, and their control there was tenuous at best. Not to mention that losing Belarus would be such a heavy blow to Bolshevik positions that they would probably evacuate the Baltics and peace out with the Baltic nationalists (just like IOTL anyway).
Lithuanian nationalists accepting a union with a "Belarusian Lithuania" which is clearly being propped up by Poland (the Litvins themselves have no chance of liberating Belarus or even growing to a major military force, so they would be reliant on Poland here) is also practically impossible.