Can I submit my new graduation marksheet in the form fill up for assistant professor post ?

You are qualified in NET last year. The validity of this certificate is 3 years for the award of JRF. The certificate is valid for a lifetime for teaching job. ALready one year is over. So your certificate is valid for another 2 years only. But you can't complete your second degree in two years. It will take three years. So after completing your second degree your net qualification is not useful for JRF. Then you have to again write the exam and year to year competition will increase. Apply for JRF with existing NET qualifications, if you got the selection it is good.
You can do another graduation after post-graduation and you can attach that marks list with your application for lecturer. But It will take three years for completing that course. Automatically competition increases. So start applying for teaching posts and simultaneously you can continue doing your second graduation also. Many reputed institutes try to appoint to recent qualifiers than who qualified earlier.
These are the points you should keep in your mind before taking a decision.

You have to be familiar with the period of validity of NEET test which is at present three year. Your planning to reappear for the graduation examination through the distance education for the improvement of scores needs additional three years. Hence during your next attempt to clear the graduation, your validity for NET test will expire. You would be required to write NET examination again with your full devotion so as to get a fair ranking.
The whole process is time consuming and during the process in clearing both NET and regraduation will eat your two years time apart from your uncertainty to get a good ranking in the test.
Hence it would be better for you to undertake the post of lecturership this time with your NET performance and start ahead for the graduation examination to clear your JRF in the next attempt.

Doing graduation again to get better percentage leading to a good overall score in the JRF / Asstt Professor selection is a good thought but it has its associated downsides. First is the validity of your NET certification for JRF for 3 years and you would definitely be losing the chance for JRF and at the most can fare better in the Asstt Professorship selection. But the question is whether sacrificing another 3 years for that makes sense or not. If you do not have any other carer choice and option then only I would suggest you to go for this plan otherwise find out some other option for making a career. Losing 3 years of this crucial time is not advisable.

Let us see what are the alternatives you have other than this one, on which you are contemplating and want our advice. Depending on your PG subject you can think of going for some diploma course which can fetch you some good job prospect. If you have done PG in Arts and Humanities then some of the areas worth exploring are Journalism, Management, Social welfare, Museum curating, Demographics etc. If you are from Science stream then some of the prospects lie in Computer programming, Web hosting and web development, Digital marketing, Chemicals and fertilisers, Agricultural field etc. If you are from commerce stream then going for some Finance and accounts package would be the best thing for entering a business house or alternatively a diploma in tax matters would be quite remunerative.

Today, many people after attaining educational qualifications are going for self employment. During the last decade some new fields have opened up which are entirely different than the old traditional ones and it is the innovativeness of the person to get something out of that brilliantly. Online businesses are mushrooming with good potential and resellers are making money just by packing the material and sending across through the courier and delivery persons. No work is being seen as menial or low if it has potential for good earning. Some tasks may require group activity also and in that case you might have to search for like minded people to make an enterprising team. So, we have to change our mindset and should be ready to face the challenges if we do not get a job of our choice due to our own low scores.