a 60 amp double pole breaker could be used for anything, a large water heater, a boiler/heat/ac unit, welder, etc, etc. lots of people put wierd shit in there basement.
i highly doubt it was used for grow lights, unless the wire was used to feed a subpanel... the breaker is to big for 'branch circuit devices' (things you normally plug in)
what you have there is a single 60 amp, 240v circuit. depending on if there was a wire for a neutral, it could be easily converted to 120v though, with a little cash and some elbow grease....
if your missing the wire for a neutral... get 240v equipement... in most cases it'll be cheaper and easier than trying to add that one wire to get a 120v neutral to the basement.
1. Where can I find this neutral wire?
2. Link or place where I can find 240 v equipment? Are you talking about the plug that runs from the ballast to the wall?
Thanks for help.