If my only income is social security benefits, but I won $10,000 in lottery winnings (taxes withheld upon receipt), do I need to file taxes this year?

It depends.  If your total income including social security benefits and lottery winnings exceed the filing requirements, you would need to file.  Please see the filing requirements.  https://apps.irs.gov/app/vita/content/globalmedia/who_must_file_charts_a_b_4012.pdf

If taxes were withheld you would want to file to get that money back.