I had trouble getting my i7-8700 65W to work in my m720q with a 65W PSU. It was working fine in Windows, but was throttling down first to 20 Watt, then to 15, 10, and finally to 7 Watt, which resulted in a maximum clock speed of 800 MHz.
The main problem seems to be a mix of crappy firmware settings from Lenovo/Intel (Reddit Post) and the weak power supply.
To fix this problem, we have to install some tools, and for them to work, you have to make sure that secure boot is OFF; otherwise, the kernel doesn't allow you to set the CPU power limits. The easiest way is to install in legacy mode; therefore, you need to disable secure boot and enable CSM in the BIOS, select legacy boot preferred.