Whisk together 2 tablespoons lime juice, 1 tablespoon fish sauce, 1 tablespoon Sriracha, 1 tablespoon soy sauce, and 1 tablespoon sweetener in a bowl to make the stir-fry sauce; set aside.
Prepare the vegetables: slice the onion into thin slivers, cut the red bell pepper into strips, and peel and thinly slice the garlic cloves.
Heat a wok or large heavy frying pan over high heat for about 1 minute, then add 1 tablespoon oil and heat until shimmery, about 45 seconds.
Add the sliced garlic and stir briefly until fragrant (under 1 minute), then remove and discard the garlic to prevent burning.
Add the onion slivers and bell pepper strips and stir-fry 1–2 minutes until they just begin to soften, then transfer them to a bowl.
If needed, add 1 teaspoon more oil to the hot pan, then add the ground turkey and stir-fry, breaking it up with a turner, for about 5 minutes.
Cook the turkey until any liquid has evaporated and the meat is starting to lightly brown.
Return the cooked vegetables to the pan, stir to combine with the turkey, and cook about 1 minute.
Add the chopped basil and cook about 1 minute more, until the basil begins to wilt.
Pour the prepared stir-fry sauce over the meat and vegetables, stir to distribute, and cook about 2 minutes more until the sauce is mostly absorbed and the dish is hot.
Serve immediately.