With your existing LMIA, you ought to be eligible for the 600 bonus points that guarantees acceptance, right? Or were you not eligible for that (maybe you have a short-term contract)?
If you're guaranteed to be chosen, or if you have a high score and you're confident you'll be picked, I wouldn't get a new LMIA permit. If it gets to be September and CIC still hasn't approved your PR you can apply for a bridging work permit to let you work until CIC makes a final decision about PR. To get the bridging work permit, you'll need to have been chosen for EE and submitted your application.
If your score is lower, and you're worried maybe you won't be picked, then yes you ought to look into a new LIMA and work permit.
