Set grill up for direct heat grilling.
Lightly brush the cut sides of avocados and lemon with olive oil. When the grill is hot, arrange the avocados and lemons cut-side down directly on the grate. Grill until the avocados are heated through and have grill marks, and until the lemons are caramelized and lightly charred.
In a medium bowl, combine the herbs with the olive oil and a pinch of salt.
Scoop some of the herb mixture onto each avocado half. Top with the toasted pine nuts and cherry tomatoes, then squeeze the grilled lemons over the avocados. Serve while still warm.