parallel interface LCDs can be connected to a parallel port directly. You will need to supply +5 V power separately. There are various programs that support output to LCDs connected this way: LCDSmartie (Windows) LCDProg (Linux) have been around for many years. Most PCs no longer have a parallel port on the back panel, but some still have a header on the motherboard. If you have one, that is actually quite fortunate, the header accepts standard 0.1" connectors ("Dupont" style) for easy wiring to the LCD.
Another option is to use an LCD with a serial (RS232/UART) interface, but those are expensive. And this also implies that you have a serial port available. Again, some PCs have only an internal header (and again, this is even better than a back panel port for this purpose).
Finally, as mentioned, there is the possibility to use a cheap Arduino clone as a USB interface module. The Arduino appears to the PC as a serial port. Any program can open that serial port and start sending bytes. The Arduino sketch will need to receive bytes on the serial port, interpret them (distinguish between commands and data to be displayed), then send the appropriate commands/data to the LCD over its parallel interface. I haven't looked, but I am sure that there are many examples of this to be found.