when did you buy the GS? It may still be under the warranty.
I had an Acura before, and Acura has a thing called Emergency Expense, basically if you replace a battery on a Sunday (when you cant take it to the dealer) all you have to do is submit the receipt (if it still under the warranty), and they will reimburse you, no need to wait to take it to the dealer
I went on a 1 month vacation to California and then Hawaii. When I came back my car started up right away. I have a 2014 GS 350 Luxury package if anything my car has all the options and more electronics so it should drain faster than your car. But to my surprise it started right away. This lead me to believe that some people have this problem while others dont. There might be a flaw in some built GS's, i think Lexus should investigate and put a TSB up or have a recall to the part or parts that is causing this premature discharge.
There have been a few instances of dead batteries in the 4GS and 3IS with the factory Panasonic batteries I believe. It has been discussed in a few threads in the past.
I think there is an ES thread also. This is strange, I left my trunk open after grocery shopping, and when I came back an hour or so later to close the trunk the trunk light was off. The last couple generations of all Lexus models have some kind of battery saver that shuts off electrical power to save the battery from discharging. This may be a bad batch of Panasonic batteries or something else. In 2008 there was a bad batch of capacitors that made their way into a lot of electronics, Samsung tv's, Apple time capsules and it caused premature product failures.