Upvote:3
Note that there are 3 international railway stations in Budapest. I am presuming that you are referring to the Budapest Keleti station which would generally be referred to as the 'main' station.
There are definitely lockers in Budapest Keleti - I saw (although did not use) them when I was there a few weeks ago.
Based on reports on the Internet it looks like these lockers cost between 400 and 800 forint per day depending on size (US$1-3/day), and can be used for up to 72 hours.