This so called battery specialist knows nothing about Toyota/Lexus Hybrids.
The 12 volt battery has nothing to do when the engine starts, and stops. It is the HV battery that provides the power to start the engine, and also keeps the 12 volt battery charged by an inverter. This keeps the 12 volt battery on charge as long as the car is in ready mode there being no alternator or starter as such as in other stop start systems where the 12 volt battery provides the engine turning power. The 12 volt battery only has to boot the computer systems (ECU's) and turn a few pumps as you put your foot on the brake, and press start. After this it is always being charged even if the engine is not running.
There is nothing special about the 12 volt battery. It does have a temperature sensor that can be gently prized out of the top and just taped to the top of your new chosen battery. This is there to help regulate the charging voltage that is dependent on temperature. Some hybrids such as the Prius use an AGM battery (absorbed glass mat) that has no free liquid acid. This is used because in the Prius, and Lexus CT (Prius clone) the battery is in the passenger compartment, and in case of a rear end accident the battery will not splash acid onto the occupants of the car.
Most batteries today are of the sealed type with a vent at one or both ends these can be fitted in the Lexus GS without any problems. If double ended vented one end vent is simply plugged with a cap provided.
Good quality batteries are available (Bosh, Varta, and many more) at around £65 with up to 5year guarantees.