Did the mechanic possibly use the primer pump to pump up fuel? Where you there when he initially started it? If he did pump up fuel with the primer pump you know what the fault was probably.

If it is running well right now I cannot think of anything to check particularily. It may or may not happen again.

Basically it does sound like you might have been out of fuel. A very tired lift pump may have had an issue with drawing fuel from a low level in the fuel tank or an issue with the screen in the tank.

It sounds like you do not do your own work. So I resist giving a course of action. That you have to pay to have done.

When I purchase any old car I go over a lot of things myself. Usually doing everything I feel is needed. Costs far less than one road breakdown. As so many old cars have not had reasonable care in respect to their age. By doing this reliability is vastly increased.

At one time the cost of paying for this service was reasonable. Almost forget it today unless you do it yourself.