NIT

It can not be done. You will not be offered admission into IIT through lateral scheme. The reason being that Indian Institute of Technology does not offer lateral entry to Engineering aspirants. It is not possible in the IITs.
It is not just the lateral entry, you will not get any sort of admission for Engineering in the IIT. To be eligible for B.Tech from the IITs you need to appear for entrance exam called the IIT-JEE which is gonna be replaced by the ISEET next year.
In order to appear for these entrance exams you must have passed 12th with PCM as the subjects. Since diploma course is taken after the 10th standard, it is also not possible for you to do so.
Therefore you should forget about pursuing B.Tech from IITs. There are number of other good universities which would offer you lateral entry, unfortunately IIT is not one of them.
Lateral entry scheme is quite popular in India. So much so that most of the universities reserve around 10 percent of the total seats for the lateral entry candidates. The admission is given on either merit or through entrance exam.
Now for admission through entrance exam you are not suppose to appear for AIEEE, IIT-JEE etc. Like I mentioned earlier, these exams are for candidates who have completed 12th. The entrance exam for you would be LEET. There are various other exams as well, some universities like to conduct their own entrance exam.
It is also possible to seek admission on merit. Various universities offer direct admission to the diploma candidates. However they require you to complete diploma course with at least 60 percent marks to do so.