There is no requirement for the larger party to have a DPM from the smaller party, that was just a convenient offer for Cameron to persuade Clegg over the line.
So, actually, both situation are possible...
Early elections can be held only:
• if a motion for an early general election is agreed either by at least two-thirds of the whole House or without division or;
• if a motion of no confidence is passed and no alternative government is confirmed by...
Parliament can vote for a dissolution... if no one is able to govern. However, I am sure the larger parties would be pretty keen to avoid being seen to be responsible for such a decision.