Just how to write software and how to do an information technology (IT) startup have evolved over the past 10-20 years due to (1) much more capable computers for much less money, (2) great progress in 'infrastructure' software, (3) the Internet, and (4) the broad idea of the 'social Web'.
So, it's possible to have a rough, maybe 'social', 'business idea', write some prototype code, see how well users like it, revise, iterate, etc.
However the old approach can remain an opportunity: Pick a big problem where a much better solution would be very valuable; find a good solution, even if implemented in software, possibly based mostly not just on routine software, wrap the solution in whatever user interface is needed, and present the result to the people who wanted the problem solved. Here are not really 'in search of a problem users would like to have solved or a business model' and, instead, did pick a good problem to begin with. Here 'lean' with lots of 'pivots' and 'iterations' is not very appropriate, and the 'lean' movement doesn't bring much that is new and good.