A serial LCD should only use a TX pin and no RX pin
Does this constructor work?
NetmediaSerialLCD(uint8_t rxPin, uint8_t txPin) : SoftwareSerial(-1, txPin) {
};
if so you saved an IO pin ...
I have looked at SoftwareSerial source, and didn't see any test to skip pin initialization in case it has a "special" value. I've put in my todo list the task of looking closer to SS code and see if I can patch it to _actually_ save a pin.
Another solution could be to shamelessly copy the tx code from SoftwareSerial and put it into a new "tx-only" SoftwareSerial class.