Then I tried to make LHA add an archive with the files in, and then extract them to my HD
It worked because lha used a sufficiently small buffer when extracting & writing the files.
When encountering this phenomenon when maxtransfer can't readily be altered, one
option is to use the shell command 'copy', with a parameter like BUFFER=60000
I think the default is 65536, but only when the device(s) being used do not specify something instead.