You cannot use the Gotek to move a lha file you’ve downloaded from the internet using another system (linux/win/mac) to the Amiga- for that you need something like Amiga Explorer. It will move it reliably but slowly. Luckily most of these files are small by todays standards.
Could you somehow move the disk image from the USB thumb drive used with the Gotek onto a host and transfer data into it with WinUAE? Mount the floppy image with WinUAE, format it, copy in the data. Then move the floppy image back to the USB drive used with gotek? On my A2500 I have a SCSI2SD, and I pull the SD card out from the Amiga and stuff it into a Windows 10 laptop. WinUAE is set to use the SD card partition as the hard drive, and it will boot the same system that runs on the physical hardware. I copied in all the WHDLoad demos and games from a directory via WinUAE into the Amiga SD card, then toss the card back in the Amiga. It's pretty flawless so far. The newer Amiga Explorer is limited in file size that can be dragged/dropped to like 10K. You have to use a CLI utility to move files over. The serial speed on the Amiga seems to max at 19200, makes the Apple II look good :-) - Ethan