Do I need my TM6 to apply for a visa extension in Thailand, and what should I do if I lost it?

The TM6 is the departure card that's (usually) stapled in your passport when you arrive in Thailand. Generally it is required for any extension of stay (depending on the immigration office, of course).

If you lost your TM6, simply file a police report, go to your local immigration office, and request a new one. The immigration office is open on Monday (tomorrow)