occurring by luck
fortuitous - lucky
A ‘fortuitous’ event is one that happens by chance rather than careful planning. How it differs to the similar meaning word ‘accident’ is that the unexpected occurrence in question is always something positive and beneficial to you. For that reason, this term has only positive connotations.
The timing of that investment is undoubtedly fortuitous. Before it was secured, we were in dire financial straits.
I stumbled across the solution to the problem through sheer fortuitousness. I was actually addressing another issue at the time.
Jack collapsed with chest pains in the middle of the restaurant, but, fortuitously, one of the other diners was a doctor.