Just to complicate things, have you considered getting a housing for your phone instead of a gopro? For more casual UW photography and video you might find it suits your needs better. It makes one less piece of electronics to carry, to charge, to get damaged or stolen.
For example, the DiveVolk housing is less expensive than traditional designs - under $200 I think - has less to fiddle with underwater, and some people love it (I haven't tried it).
The decision about lights or no lights remains the same in either case. If all you want is a video log of your dives then you may be happy without lights. If you want photos or video of coral or critters up close (closer than say, 1 metre), especially deeper than say 5 - 10 metres, you probably want a light. Underwater images will ALWAYS have better colour rendering when you supply the missing wavelengths in the blue-green-filtered sunlight. But that's not as important as whether or not you care (or even notice) the difference compared to images taken in natural light (maybe with a filter) and post-processed in software to "correct" the colours.
Of course it's up to you: I'd say go ahead and get the gopro (or phone housing) you want without lights, and see how you feel about the results after your next dive trip. If you're not satisfied with the colour, then think about spending more money to get lights for next time.