Do I need an LLC to run a website?

No. You can build and run a website as a sole proprietor with no LLC at all. Plenty of small business sites launch this way, especially early on.

An LLC matters for liability protection and how you get taxed, not for whether you're allowed to have a website. If you're selling products, taking payments, or worried about personal liability, that's a conversation for a lawyer or accountant, not a web design decision.