If a join a new lodge before demitting from the mother lodge, will I still need to go through the initiation ceremony again at the new lodge? And how demitting from mother lodge after joining a new lodge is different from demitting from the mother lodge and then joining a new lodge?

Initiation into Freemasonry is performed only once. A Master Mason joining a new lodge enters as a joining member or by affiliation rather than undergoing the initiation ceremony again, as the United Grand Lodge of England notes. While the administrative process of applying by petition, investigation, and ballot applies to affiliation much as it does to initiation 1, the degree ceremonies themselves are not repeated.

The procedural difference between the two sequences turns on the Mason's membership status at the time of application and the standing required on his clearance certificate:

When joining a new lodge before demitting from the mother lodge, the Mason applies under plural or dual membership 1. He remains an active subscribing member of his mother lodge and must produce a clearance certificate or certificate of good standing confirming that he is free of arrears and in good standing 1. If he subsequently demits from the mother lodge after his election to the new lodge, he simply submits his resignation to the mother lodge, leaving his active membership established in the new lodge 1.

When demitting from the mother lodge first, the Mason severs his active affiliation before applying elsewhere. His mother lodge issues a demit—a clearance certificate confirming his resignation while in good standing and free from charges or debts 1. He then approaches the new lodge as an unaffiliated former member rather than an active dual member, submitting that certificate of regular dismission along with his petition for affiliation 1.