How to transmit serial data from laptop USB out to Teensy?
Your second option is the easiest.


  a usb to ttl adapter cable to go straight to the Teensy LC, but I read somewhere that the serial UART with Arduino is different in some way


Without seeing what you read, perhaps they were just talking about the fact that the Arduino is not "true" RS-232, it's only at TTL (or 3.3V) levels.


  and wasn't sure if the serial communication coming through the usb to ttl cable would be compatible with the Teensy.


It should be compatible, especially since you note that the Teeny is 5V-tolerant.


  I was looking at one of these cables at sparkfun, and I think I would connect the TXD from the cable to the RX on the Teensy, the RXD from the cable to the TX on the Teensy, and the GND cable to a ground on the Teensy.


That's it in a nutshell!