The light cruiser will only appear in the ship store if you have used the free promotion token for a Lt. Commander level ship. (This helps to keep new players from accidentally picking this ship again when they should be upgrading at low ranks.) Check one of the Lt. Cmdr. level ships and see if it lists its cost as a free ship token that you have. If so, select one. (This would be the Saber-class escort, the Nova-class science vessel, or the Vesper-class cruiser, or one of the variants of those). Once you have used that free ship token, close the vendor window and speak to Lt. Laurel again, and see if the light cruiser appears in the listing.
IT WORKED!, I CAN NOT BELIEVE IT IT WORKED!, i need some dilithium because right now i am a little short BUT I CAN COMMISSION A FRIGATE NOW!
Thank you VERY VERY much for solving this issue, you have no idea how long i wanted to had my frigate back, how frustrating it has been all this time.