I think many people who argue against a second referendum have not taken on board the scale of the difference between the various Brexit options. We could retain access to the single market and free movement of labour (the Norway option). Or we could just cut a trade deal with the EU, do nothing on services, and end free movement (the Canada option). Or other things in between. In economic terms the Norway option is much closer to EU membership than it is to some of the alternative forms of Brexit.
Perhaps an analogy is that you decide one day that it is time to move house, as you are really bored with your current property and aggravated by its various imperfections . That decision is akin to the Brexit vote. But you have no idea where you are going to move to. It could just be a local move to a similar style property, or it could be to somewhere in another part of the country where property is cheaper but where you would have to find new friends and a new job.
The Brexit vote in practice is the green light to explore what possible alternatives are available. Having looked at the various alternatives, you may decide that you do indeed want to move. Or alternatively you may realise that your current house is not so bad after all, and is superior in many ways to the best available alternative, and so you decide to stay. To deny a second referendum is a bit like saying that once you have decided to move you cannot go back on that decision, no matter what the alternatives turn out to be. A slightly closer analogy is that you decide to move house, but then you get someone else to choose the best new house for you, and you have to accept the choice they come up with even if you think it is inferior to your current house..
So the key arguments for a second referendum are that the alternative to EU membership was not specified in the first referendum (they were also unknown at the time, and depend on what can be negotiated from the EU), and that these alternatives are very different from each other. I cannot see the logic in saying people should have a direct say on whether to leave the EU, but no direct say on what to leave it for. 
 I choose an analogy involving an individual rather than a group or society as a whole to avoid the (well known to economists) problems associated with non-transitive preferences for groups of individuals: see Jonathan Portes here.
 Note that I make no reference to voters being lied to in the first referendum. My argument still holds even if Leave had been completely honest.