What are the future prospects of ocean engineering at IIT Madras, assuming I want a lucrative position somewhere?

As there is no exact definition of a lucrative position, I will answer this question objectively. Firstly, there is no comparison between MTech and MBA as the latter has excellent job prospects while MTech does not.

As far as the Ocean Engineering department of IIT Madras is concerned, you definitely will have great career prospects after graduating from this department. The faculty are experts in their respective fields and because of the small size of the department, you get to interact much better with them.

But if we talk about placements, core companies offering roles are very limited, almost zero. This is a very specific branch and has limited opportunities to offer. This situation is similar in most MTech branches other than CSE and Electrical. 

If you are genuinely enthusiastic about this branch, let me tell you this department has excellent research opportunities that will satisfy you. Anyone who prioritizes research over placements will find this branch to be pretty good. We can say that the prospects vary from person to person depending on an individual's commitment to the discipline.

will find this branch to be pretty good. We can say that the prospects vary from person to person depending on an individual's commitment to the discipline.