Melt the butter, add the garlic and cook until aromatic (about 30 seconds).
Add the milk, and stir with a whisk to deglaze the pan.
Stir in the chicken stock, lemon zest, salt, pepper, and orzo.
Bring to a boil, reduce the heat to low, and simmer covered (occasionally stirring) for 8 minutes.
Stir in the spinach and allow to cook until the spinach is wilted and the orzo is al-dente (about 7 more minutes). If it looks too dry, add more stock or milk to loosen.
Remove from heat. The sauce may be a little thin but will thicken as it cools.
Mix in the cheese and lemon juice. Taste for seasoning and add more salt as needed before serving. Serve immediately to avoid drying out the sauce.
Notes
The liquid quantities may vary depending on the heat of your stove, so keep an eye on it as it cooks. If it looks like it needs more liquid, add a little more stock or cream. If it seems too wet, let it sit for a bit longer, and the pasta will soak the excess liquid in a few minutes.