Lukashenka refuses to acknowledge the DNR and LNR as legitimate. He also has problems with Crimea's status. And a lot of the economic nonsense Russia's been doing with Ukraine for the last number of years.
At the same time, Belarusian is a threatened language because under Soviet rule Russian was more and more important and pushed Belarusian aside. Exactly what would have happened in Ukraine if not for the parts of Ukraine not under Stalin's rule for the first decade or so and if not for the "fascist nationalists" that wanted to preserve their language and culture. (This, of course, makes a lot of Latino activists "fascists" and a lot of Native American groups "fascist".) Belarusian is often taught like French is in the US: Yeah, you take a year or two of it, but it's not a language you (a) speak, (b) remember, (c) care about.
A lot of Belarusians are pro-Russia and are "Russian speaking". That, as far as Putin is concerned, makes them people that he is personally responsible for and in charge of.
Worse, Belarus was Russian imperial territory. Smolensk was one of the Kievan Rus' cities. Large parts of the country weren't in the province of Belorussia under the tsars. All the business about "Novorossiya" being properly part of Russia holds even more true for large parts of Belarus'. (I suspect that Lukashenka would also be anxious in that while Germany from time to time makes noises about how improper the loss of Czech and Polish territory was, and some countries like Hungary have made noises about territory given to Ukraine, Poland could say the same thing about a large strip of Polish territory now part of Belarus'. Post-WWII "reparations" to Stalin included territory and people.)
And, unlike Ukraine, Belarus' has Russian troops stationed on it. With less of a separate Belarusian army than even Ukraine had.