Rinse the rice under cold water at least three times until the water runs clear, then drain using a fine-mesh sieve.
Heat the vegetable broth in a small saucepan until it is simmering or steaming, then keep warm.
Place a large skillet or shallow pan with a lid over medium heat and add the butter and oil; melt together.
Add the orzo and stir to coat in the butter and oil, then cook for 4–5 minutes, stirring occasionally, until the orzo is golden brown.
Reduce heat to medium-low and add the finely chopped onion; sauté gently for about 4 minutes until softened.
Add the chopped garlic and drained rice, stirring until the rice grains look opaque and bright white.
Pour in the hot vegetable broth, add salt and pepper, and bring the mixture to a gentle simmer.
Reduce heat to low, cover the pan, and simmer for 20–25 minutes until the rice is tender and the liquid is absorbed.
Remove the skillet from heat and let the pilaf stand, covered, for 5–10 minutes without lifting the lid.
Fluff the pilaf with a fork, sprinkle with lemon juice, and serve.