This sounds like your battery is either discharged, or defective; or the battery cable clamps have become corroded (on the inside surfaces, which cannot be seen when looking at them). The first thing to do is to remove the battery cable clamps, and thoroughly clean the battery posts and the inside surface of the clamps with a professional type battery clamp cleaning tool. Then put the cables back on, and tighten the clamps securely.
If the lights still go out when you try to start the car; have the battery recharged and then tested with a load tester. (A voltmeter cannot be used to properly test a car battery; the battery must be placed under a load which is similar to what the starter would draw). If the battery fails the load test; it will have to be replaced.