Not really. If you have enough payload to LEO you can also throw something to TLI, just less. All commercial rockets like Falcon 9 or Atlas 5 can throw lots of

Not really. If you have enough payload to LEO you can also throw something to TLI, just less. All commercial rockets like Falcon 9 or Atlas 5 can throw lots of payload to the moon as well. Even tiny rockets like Rocket Lab Electron have launched moon missions. Now what is true that the further out you go, a hydrogen RL-10 based upper stage will win out better then a Falcon 9 based kerlox upper stage. So while the payload to LEO between rockets can be pretty close, the payload to a moon orbit can be quite different.