You can find life data here:
http://www.pkpd.lt/lt/border
"Prognozuojamas laukimo laikas" column is the one you are interested. It shows expected wait time in hours. Medininku is generally very busy at any time. But it's most convenient way from Vilnius.
On border check your car and anything on you can be inspected by both Lithuanians and Belarusians. On entering Belarus you will have to fill declaration. It's just to state that you are bringing with you. Sometimes officers try hard to get a bride. My advice is to not to pay. Police in Belarus is corrupt and can try to scam. Lithuanian cops can to, but not that often.
If you want trouble free and convenient day trip get a train or a bus.