If you are running the 64 bit version of the software, Ableton Live can use as much RAM as your computer has to supply or Ableton Live needs. Having a computer with at least 8GB of ram is recommended, especially if you intend on using third party plugin-ins
According to an article on Ableton’s site:
“Due to persistent out-of-memory crashes during use, Ableton will discontinue the 32-bit version of Live for new updates of the software from late 2017. The 32-bit version of Live (like all 32-bit applications) can use a maximum of 4GB of RAM only, which can quickly be exceeded when using large multisamples or memory-hungry plug-ins, resulting in crashes.”
Ableton Live will tell you whether you have 32 or 64 bit upon opening Live in the gray splash screen that appears while the program loads. If you have 32 bit, please consider upgrading.