Well there are three complications with fitting another CPU in the Laptop.
The first one would be that the CPU is indeed soldered and not held in as you stated above. To be 99% sure is really strange because as far as I know no Laptop of Lenovo came with a normal socket in all their IdeaPad Lineup.
A soldered CPU is still exchangeable, but it requires equipment to desolder the old CPU and then to solder the new one. That is not something you can do with a simple soldering iron, but some Laptop-Repairshops have the option to resolder a BGA CPU.
The second problem is the Lenovo BIOS. This company is known to implement White- and Blacklists into the BIOS(UEFI) to only support specified Hardware. Hardware that is not on the Whitelist just won't start.
The third problem would be Chipset, Power and Thermal concerns. Even if there is a FX processor that is designed for the FP4 BGA Socket, and you can solder it somehow, and Your BIOS hat the correct Microcode to support it and there is no Blacklist in the BIOS. Then the board still doesn't come with a compatible Chipset to support the CPU and the Power supplied to the CPU would not be enough, cause the FX lineup consumes much more power, and there would be Thermal Problems, because a FX CPU produces a lot of more heat than the small A6 CPU, and the cooling would not be enough.
As you can see, it is simply better to live with what you have or buy a new Laptop entirely.