Belarus is a Russian military ally housing Russian aircraft and strategic land connections leading to Moscow. We'll be hit on day 1 if shit hits the fan.
Also, pardon me if I sound flamey, but the popular sentiment stating that the West can easily win a conventional war with Russia is very much present, among both ordinary people and Pentagon strategists, and that is really dangerous.
Actually my money would be on Lukashenko having enough brains to declare Belarus neutral, and then either wait out the whole war or put up some token resistance against Russian occupation. This would not necessarily mean that no Belarusian territory will get nuked, but it will make it less likely.
And why do you think the West would be unable to win a conventional war against Russia?
While the West (and by West I mean NATO) certainly can win a conventional war against Russia, in theory, there are two complicating factors:
1) The difficulty. Russia is stronger than all opponents that NATO has recently faced, and also has lots of advanced capabilities that counter some of the more advanced tech NATO has. Thus, lots of tactics that worked against Middle Eastern or North African armies are not going to work so well against Russia.
2) Casualties. Most other tactics that would work well against Russia involve taking a lot of casualties (in large-scale ground assaults), which doesn't mesh well with the casualty-averse nature of the Western society. The ones that are left have a problem of taking a lot of time.
So in essence, even without taking nuclear weapons into consideration, beating Russia in a conventional war, while possible, is either going to take a shit-load of time, or will take a lot of casualties to achieve. First one is not really possible because democracy tends to switch governments over large periods of time to a more popular one (which in this case will be the one that makes peace), the second one will lead to mass unrest and - likely - the forcible change of government to the one that makes peace.
There's also the "blitzkrieg" tactic, which can be both fast and without casualties, but it's the one that has the highest chance of triggering a nuclear response, so it's not likely to be actually used.