Heat a large pot over medium-high heat. Add oil and heat until shimmering. Cook lemongrass and onion, stirring frequently, until onion begins to caramelize and turn golden, about 8 minutes.
Stir in chiles, coconut milk, wine, fish sauce, and herb stems. Bring mixture to a simmer.
Add mussels and cover pot. Cook until mussels open wide (discard any unopened ones), 4 to 5 minutes.
Transfer to a serving bowl. Sprinkle with herb leaves. Serve with lime and rice.
*Find arbol chiles in Mexican markets or your grocery store's Latino-foods aisle. If the mussel "beard" (stiff threads protruding from the shell) is still attached, pull it off.