Preheat the oven to 180°C, 350°F.
Pat the lamb dry and season generously with salt and pepper.
In a large heavy pot or Dutch oven, heat the olive oil over medium-high heat.
Brown the lamb pieces on all sides until nicely golden. Do not overcrowd the pot. Work in batches if necessary.
Remove the lamb and set aside. In the same pot, lower the heat and add the chopped onion.
Sauté until soft and translucent. Add the garlic and cook briefly until fragrant.
Deglaze with the white wine, scraping the bottom of the pot to release any browned bits.
Let the wine reduce for a few minutes. Return the lamb to the pot and add enough hot stock to almost cover the meat. Cover and transfer to the oven.
Cook for about 1 hour to 1 hour and 15 minutes, or until the lamb is tender but not falling apart.
Remove the pot from the oven. Stir in the kritharaki and add additional hot stock if needed. The liquid should just cover the pasta without looking like soup.
Return uncovered to the oven and bake for about 20 to 25 minutes, stirring once halfway through, until the kritharaki is tender and most of the liquid has been absorbed.
The texture should be glossy and slightly creamy, not watery. Remove from the oven and let the dish rest for 10 minutes. The kritharaki will continue to absorb liquid and settle.
Finish with freshly squeezed lemon juice, adding gradually and tasting as you go.
Adjust salt and pepper if needed.
For a silkier finish, you may stir in a small knob of butter at the end.
Serve warm with extra lemon on the side and a simple Greek salad.
