So, if I am understanding correctly. LMIA Exempt jobs are always tagged with LMIA Exempt Work Permits and can not be correlated as Open Work Permit + LMIA Exempt Job offer?
Not sure what you are asking. LMIA-exempt work permits can be either open or closed, where closed work permits have the employer named on the permit and the holder cannot change jobs without obtaining a new work permit. Those with closed, LMIA-exempt work permits MAY be eligible to claim the points for a valid job offer, if they can meet the other requirements as well. Open work permit holders are not employer-specific, so require an LMIA to be eligible for the valid job offer points.
If in the best-case scenario, if I will get a new job from the market then I still have to request a new employer for supporting me with LMIA. Is this a common procedure that any employee of a Canadian company supporting NOC 0,A,B type of work can request their employer to support with an LMIA during their work tenure which can support CRS. Or I have to look for LMIA approved job offers (if any position available) and then join a new organization, which can boost my CRS score.
There are two types of LMIA, although the application process is the same PITA - one is to support a temporary work permit application, costs CAD 1,000 and can also be used to support PR applications. The other is to support PR applications only, and has no fee. So to answer your question, the fee-free LMIA is a good option for open work permit holders, but it does require an employer being willing to support the process.
Do, I need to appoint a lawyer to get all the detail clarified or any website link available which can have all the necessary clarity.
All the information you need to apply for PR is on the IRCC website. scylla has given the link for the LMIA. The rest is entirely up to you.