I see. This is the danger of wikpedia (unsourced internet) and badly applied figurative language, apparently repeated by the FIFA (football) website. "Basketball War" in this case is entirely hyperbole.
There was no war between Latvia and Lithuania. There was not so much as a border incident.
What did happen : The 1939 Eurobasket (3rd European basketball championship) in Kaunas was won by Lithuania over Latvia 37-36 on the last basket. That shot occurred after time had run out, but the referee had not blown the whistle and counted the shot (accounts differ of course). Latvia protests but Lithuania is declared the winner. Conspiracy theories and acrimonious accusations.are made, it seems some regular sports events got cancelled that year.
Never heard it called "Basketball War" before. You are not confusing it with the actual so called "Football War" between Hondura and El Salvador in 1969?