How can LMT be converted to UTC time?
You have almost solved the problem yourself. The website you linked to does not help you because, for some reason, it assumes Local Mean Time (LMT) to be equal to UTC. For your problem, LMT needs to be for 85° of East longitude. So, ignore that website and let's move on.

For every degree of longitude, you calculate 4 minutes of difference from UTC. You have already correctly calculated the LMT difference from UTC for 85°E:


  First of all, what I've done is converting longitude into time as
  follows: $$t=85\cdot4=340\hspace{1mm} min=5h\hspace{1mm}40m$$


This leaves you with the question of whether to add or subtract this difference, as you stated:


  But then, in order to compute the UTC time, what do I have to do, either adding up this time to the current LMT or subtract it (and what is the reason)?


Let me start with the reason—the explanation of why we want to either add or subtract the difference between LMT and UTC—and then give you the solution.

LMT can be thought of as roughly equivalent to time based on the Sun's position. It is not equivalent to that, which is Solar Time, but it is related. Keeping that approximation in mind, consider the difference in time between when the sun reaches solar noon over Delhi, and when the sun reaches solar noon over London. As the earth rotates, the sun reaches solar noon first over Delhi, and then, a few hours later, over London. Thus you know that UTC will be a few hours behind Delhi LMT. This means that you need to subtract the calculated difference between LMT and UTC.

Another way to put this is: LMT for East longitude is ahead of UTC (subtract the difference to find UTC), and LMT for West longitude is behind UTC (add the difference to find UTC). Thus a more proper way to perform your calculation mathematically would be to properly incorporate the negative sign:

$$t=-85\cdot4=-340\hspace{1mm} min=-5h\hspace{1mm}40m$$

Therefore, if the LMT in Delhi (LON=85°E) is 17:45, then:

$$UTC=12h05m$$