Hi Israeli ~
The diet as you described in the Garden of Eden ended when Adam and Eve sinned, and they were cast out of the Garden and into the world. Basically, humans then became part of the food chain and as such, omnivores. Once they partook of the forbidden fruit, everything that had existed in the Garden of Eden changed for mankind.
Even Christ Himself dined on fish and presumably beef at feasts, where fatted calves were slaughtered for such occasions. I would imagine He would have also enjoyed lamb meat, goat meat, various poultry and other seafood, plus all of the wonderful by-products made from the milk of cows and goats.
I'm sorry to hear that you are having trouble getting motivated and staying on course. I guess your question of how one does a birthday without it turning into a prolonged lapse of eating LC (or a binge) depends on each individual person...their desire to cheat in the first place, their tolerance for occasional treats, their desire to return to eating right, and their will to not give into the mindset of "well I blew it today, might as well wait until tomorrow, or Monday, or the 1st day of the month," etc.
Just because it's your birthday does not mean that you MUST go off of your low carb way of eating. Instead of cake, you can treat yourself to something luxurious that you don't have very often, like perhaps lobster or snow crab or whatever delicacies you eat in your part of the world. There are also some LC desserts that can be enjoyed, such as LC cheesecake.
You have options. You just have to have the willpower and hopefully, the support of family and friends (like us here!) to help you stay the course on your journey.