No, Lyme disease is entirely treatable in the first days following the infection. You can get it multiple times and treat it every time.

Once you don't treat it for a few days, you'll have it for life and that's when it gets nasty.

This is untrue. Borelliosis is treatable at any time: it's caused by a spirochete very similar to syphilis. The second time I had it it was diagnosed about 10 months after infection began, and a simple course of 100 mg Doxycycline for 21 days was all it took.

It's true that (a) sometimes an advanced case where the bacterial infection has spread to the brain requires a stronger intravenous antibiotic that will cross the blood-brain barrier and (2) the infection can cause permanent damage to the joints, heart, and even the brain. But the latter is no longer Lyme disease, it's just arthritis, heart disease, or brain damage and has to be treated symptomatically. You no longer have Lyme though.