I read Application Guide for Foreign worker stream,Yes, once you got an Approved LMIA you will be eligible to apply for a Work Permit regardless of where you are (outside/inside) Canada.
Sorry I'm not sure what will be the advantage of LMIA with regards to OINP. My knowledge is very limited, I'm only sharing what I have learned in my personal experience.
If you want apply for the Ontario Immigrant Nominee Program , you have to see if you are eligible to the programs they offer, here's the link: https://www.ontario.ca/page/ontario-immigrant-nominee-program-oinp ,
Below lines suggest, the successful application will get nomination certificate which gives you 600 points.
This is not paper based but online. Can someone please confirm on this ?
And any rough idea about processing timelines ?
If your application is successful, you will receive a Letter of Nomination and a work permit support letter, along with the OINP Confirmation of Nomination document. Successful nominees must submit an application for permanent residence to IRCC within six (6) months of being nominated by the OINP. You must include a copy of your Letter of Nomination and a copy of the OINP Confirmation of Nomination document. Note: Nomination by OINP does not guarantee the approval of your application for permanent residence by IRCC.