Do I need to apply from home country?

Hi, you can try to convert your current L type to a work Z type at the exit and entry administration of the local PSB within China. If it can be done, you don't need to leave China.
You should prepare the relevant documents including your passport and its copy, the application form, a passport-style photo, valid registration form of temporary residence, invitation letter and employment permit, as well as other required documents. Then, submit the application to the local PSB.