Could be the starter or the solenoid. You never said what you thought fixed it. The starter could have a bad spot on the comutator and that would cause intermitent problems.
I would turn the lights on and see if they are bright.
If not I would check all connections again.
If they are bright I would try the starter and see if the lights go real dim.
If they do I would suspect the battery or starter.
If they don't I would suspect the cables, connections, solenoid.
Does it do the same thing if you jump it across on the solenoid?
I might even pull the starter appart and inspect it. If you do the brushes can be difficult to get back in.
I would turn the lights on and see if they are bright.
If not I would check all connections again.
If they are bright I would try the starter and see if the lights go real dim.
If they do I would suspect the battery or starter.
If they don't I would suspect the cables, connections, solenoid.
Does it do the same thing if you jump it across on the solenoid?
I might even pull the starter appart and inspect it. If you do the brushes can be difficult to get back in.