Firstly, It should be noted I've not tried this with bikes and I believe bikes are a little different in their criteria for price since a 15k bati RR is apparently too hot to handle.
This is also not official in anyway, this is purely my theory from observations.
1. It appears that the sale price of a car to LCS is 10% of the car book value. The way I've thought about this is that a car I usually sell to LCS is the Oracle, this is 80k new from the internet and in mint condition sells to LCS for 8k. This also seems to be true with other cars (the baller sells for 9k and is priced at 90k new) so I'm confident this is correct.
2. The threshold point I believe is 99,999$, again, the reasoning in this is that a baller can be sold for 9k and has a book value of 90k but a comet with a book value of 100k and following point 1 therefore has a sale price of 10k cannot be sold to LCS.
3. It's said that the 'cooldown' period is 30 minutes between sales, I'll test this at some point to confirm it
4. If you 'own' a car and wish to sell it it's book value must not be above 50k.
In light of this here is a list of what I believe are the best cars to sell to LCS and the prices you'll get from them:
Lampadati Felon GT = 9.5k
Gallivanter Baller = 9k
Lampadeti Felon = 9k
Obey Rocot = 8.5k
Ubermacht Oracle = 8k
Benefactor Schwartzer = 8k
Albany Cavalcade = 7k
Ubermacht Zion Cabrio = 6.5k
Ubermacht Zion = 6k
One car I have yet to try to sell is the Lampadati Felon GT, this has a book price of 95k so in theory will sell for 9.5k and be the most profitable car you can steal and sell to LCS, someone will have to confirm this first though. < Confirmed