If you have enough RAM memory, place the received string in a RAM buffer. You can access the buffer when you need to refresh the LCD.
This approach will make your program more modular: one routine to receive and place in the buffer; one routine to display the buffer contents in the LCD screen.

Most LCD alphanumeric screens include more memory than what can be displayed. You can use this memory to save messages and use shift commands to display the portion you want. But I don't think this is a good option.

Regards,
Alfredo del Rio.