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You wouldn't be looking for sources of LS Car Meet reputation if you didn't purchase the membership so I'll skip that part. Earning the reputation is kind of glanced over in-game so here is a breakdown of what you can do to increase it.
Daily logins
These are self-explanatory - get into GTA Online and you will get a reputation bump once a day.
Test Track
LS Car Meet offers the ability to check out a selection of cars you may have not obtained and doing so will increase your reputation periodically. If you find driving around an empty parking lot boring, you can open the Interaction menu and start the Time Trial to try and score better lap times. This is especially useful if you're testing your own car and trying to push its limits. It helps become more effective with it in races and other activities as well.
Street races
If for some reason you didn't check these out, please do. They are a great refreshing addition to the existing races in GTA Online so you will do yourself a favour twice since they can yield reputation as well.
Being at the Car Meet
It might sound weird but just being around the warehouse will increase your reputation periodically. Unfortunately, you can't just tab out and do something else to let the reputation rise since GTA Online will kick you in just a couple of minutes of inactivity. Checking your unlocks out at the merch and tattoo shops, however, can be a good thing to do from time to time so make sure you visit them in order to passively rake in reputation points.
GTA Online by Rockstar Games and Take-Two Interactive
