Preheat the oven to 375°F.

In a bowl, combine ground lamb, egg, and breadcrumbs.

Season the mixture to taste.

Mix the ingredients well.

Divide the mixture into 4 equal portions.

Shape each portion into a burger patty.

Heat 1 tablespoon of olive oil in a frying pan over medium-high heat.

Cook the burgers for 2-3 minutes on each side, until browned.

Transfer the browned burgers to a roasting pan.

In a separate bowl, combine feta cheese, chopped black olives, and half of the chopped thyme.

Spoon the feta and olive mixture over the burgers.

Bake the burgers in the preheated oven for 10 minutes.

Heat the remaining olive oil in a saucepan.

Add the sliced red pepper, yellow pepper, and finely chopped red chili to the saucepan.

Fry the peppers and chili for 4 minutes, stirring occasionally.

Add the remaining chopped thyme and zucchini strips to the saucepan.

Cook for 5 minutes, or until the zucchini is tender.

Season the pepper and zucchini mixture to taste.

Serve the cooked burgers with the pepper and zucchini mixture.