Hey,
you can use command 'bacct -u <username>' to see how many exited Jobs there are.
Another way is to search at the accounting files. Under your platform directory '../lsf/work/<clusterXX>/logdir' you should normaly find some files 'lsb.acct'. Maybe they have a numeric extension.
These files hold a record per Job, so you can search for the user you are interested in.
I process these files with SAS so we have a history of the Grid jobs.
Greetings
Andreas
bacct - command reference
https://www.ibm.com/support/knowledgecenter/en/SSETD4_9.1.3/lsf_command_ref/bacct.1.html
lsb.acct - file reference
https://www.ibm.com/support/knowledgecenter/en/SSETD4_9.1.3/lsf_config_ref/lsb.acct.5.html