Does LSF support array jobs? In GridEngine aka SGE I would submit one array job running 100 instances and depending on the index $SGE_TASK_ID you get for each job it could honor the relevant lines of the master.txt file. The problem I see with your solution is, that you would need either 100 different data1.txt files, or to wait with the next job until the predecessor finished (to avoid overwriting of the previous data1.txt file).
Aha, LSF has the variable LSB_JOBINDEX, so:
echo "I will handle lines from $START on."
sed -n $START,+99p master.txt > $TMPDIR/input.txt
and submit with bsub -J "data[1-100]" script.sh
(I have no access to LSF, but I think you get the idea). The $TMPDIR should be created by LSF unique to each job.