In a small saucepan, combine apple cider vinegar, water, sugar, and salt. Bring to a simmer over medium heat, stirring until sugar dissolves. Remove from heat and add sliced red onion. Let it cool for at least 30 minutes.
In a large bowl, mix ground lamb, cumin, coriander, smoked paprika, cinnamon, salt, and black pepper until well combined. Form the mixture into 8 equal patties.
Heat olive oil in a skillet over medium-high heat. Cook the lamb patties for about 4-5 minutes on each side or until they reach an internal temperature of 160°F.
While the patties are cooking, toast the slider buns in a separate pan or under the broiler until golden brown.
Assemble the sliders by placing a lamb patty on each bun, topping with crumbled feta, a handful of arugula, and a generous spoonful of pickled red onion.
Serve immediately.