I have the same issue, I have spent about two hours this morning trying to find the info on Adobe website, the chat line couldn't help. I went into Manage my account and all this did was the same as the rest of Adobe, just went round and round in circles. Its a big joke. I'm certainly NOT impressed with after sales service.
Sign into your Adobe Account that you used to purchase LiveCycle with. Go to the manage account section. Find the plans and products section and click on view your orders. The download link should be visible for the product purchased.