The tuning system of "Equal temperament" used today was mostly a Classical era development. Prior to that the most used system was something called "Meantone". The purpose of meantone system was to preserve the consonance of the 3rds rather than the 5ths as in the modern Equal temperament system. The musical aesthetic was different than today and is partly reflected in the tuning in use at the time.
For fretted instruments, movable frets was the best way to deal with the various tunings available and to adjust the thirds for different keys. The most common tuning used was the quarter (1/4) comma meantone but there were others 1/5, 1/8...
Here is an article on the subject. In table 2 you can see the various "temperaments" and their cent values.
2handband, the only time tied frets slow one down is if the left thumb is planted heavily against the neck. I'm sure you don't play that way as that would also seriously hinder a guitarist as well. In actual fact, when playing the lute, I don't even notice the feel of the frets on the back of the neck. Trust me
you will have no problem.
Bridges with a compensated saddle changes drastically the sound of a lute. Compensation for intonation is adjusted at the fret level which is something guitars with fixed frets have been struggling with since the inception of the fixed fret. The movable tied frets of the lute would actually be a blessing for guitarists should they decide to switch...but we all know that is never going to happen.
A good lute player can compensate for intonation at the bridge by adjusting where they place the loop. There is plenty of room for fine tuning should the need arise but mostly it is taken care of with the frets.