Is it possible to upgrade the processor on the lenovo flex 2?

On some laptops it is possible to upgrade the CPU if they are socketed. However it may not be advisable, often the laptop has to be completely dismantled to get to the processor and you risk damaging many of the delicate cables and connectors if you are not used to doing this sort of thing. Also you may be running the laptop outside of the manufacturers intended specs, so a faster processor often generates more heat so the fans may be working harder and more noise, the battery life will be less if there's a higher power draw, the BIOS may not recognise the different CPU.
Most laptop CPUs are not sold direct to the end user only to the trade or manufacturers. As most of these CPUs are not current, then you would have to source off eBay or amazon. Finally most workshops would refuse this sort of work as you would be taking the laptop outside of the recommmended specs.