My CH340 works for FastLynx 3, but not for Laplink.
Well, it will be one cause.
Even if you create a serial Laplink cable, I still think that the CH340 (or any other USB/serial adapter) will be a problem for Laplink.
Laplink worked when I switched to using the serial port on my modern motherboard.
The serial version of the Laplink cable is the same serial cable used for FastLynx and Intersvr/Interlnk.
There are many pinouts on the Internet.
One is at
http://pinouts.ru/SerialPortsCables/laplink_cable_pinout.shtml