Bash background execution not returning

If the csv files are generated by the java command, this will fail because the mv will run before any files have been generated. Since all java processes are sent to the background, the loop will finish almost immediately, so the script continues to the mv which finds no files to move and so does nothing.

A simple solution is to use wait. From help wait (in a bash shell):

$ help wait 
wait: wait [-fn] [-p var] [id ...]
    Wait for job completion and return exit status.
    
    Waits for each process identified by an ID, which may be a process ID or a
    job specification, and reports its termination status.  If ID is not
    given, waits for all currently active child processes, and the return
    status is zero.  If ID is a job specification, waits for all processes
    in that job's pipeline.

The relevant bit here is "If ID is not given, waits for all currently active child processes". This means that you can just add wait after your loop and that will make the script wait until all child processes are finished before continuing:

#!/bin/bash

for f in ./lqns/*.lqn
do
    java -jar DiffLQN.jar "$f" &
done

wait

mv ./lqns/*.csv csvs

Alternatively, you can combine the java and mv commands:

#!/bin/bash

for f in ./lqns/*.lqn
do
    java -jar DiffLQN.jar "$f" && mv /lqns/*.csv csvs &
done

Another, possibly better, option is to use GNU parallel (which should be in the repositories of whatever operating system you are running), a tool designed for precisely this sort of thing. With it, you could do:

parallel java -jar DiffLQN.jar ::: ./lqns/*.lqn
mv ./lqns/*.csv csvs