It will always end with the gravel/soil/lawn being driven out...
Well, then I’ll propose a crazy idea: don’t use the finest possible gravel, but rather coarser gravel, and apply it finely moistened with an adhesive. As a result – although I lack the basis for speculation on durability – I would expect the following: after filling in, a hardening of the adhesive bridges at the contact points and thereby stabilization of the “macromolecule” in each lawn stone cell – thus a significant reduction of the loss – with the coarse structure providing plenty of space for seepage. The adhesive would of course have to be stable, also regarding no water solubility of the contained substances, so as not to contaminate the passing precipitation. Maybe a topic for “Youth Researches” / MMM