I am not a Lyme specialist.

But I can offer some general information about the actions of some drugs.

Doxycycline is part of the tetracycline family. It is a bacteriostatic agent.
That means it stops bacteria from growing/mulitiplying. It does not kill. It is still useful however in many diseases.

Cephalosporins and penicillins are examples of bactericidal agents. They kill outright.

So the article above is correct in some statements. What I do not have is the skill to comment on is how that impacts Lyme. In general bacteriostatic agents rely on the body for removing the intruder by the immune system.

I do not know if once Lyme is entrenched in tissues what antibiotics should be used. Certain ones do not penetrate well into some areas. Others do.
Cephalosporins like Rocephin are typically used for tissue infections following surgery/trauma. But they do not penetrate fluids well such as sinuses or middle ear fluid.

The value of doxy in general in medicine is its broad spectrum of action against many things, including anthrax. So I know it is a proven drug for many things. I just don't know where now in the Lyme community it stands.

Alot of changes have occurred in Lyme treatment, over the years. So I would have to defer to your infectious disease specialist on this question.

Antibiotic therapy that continues can deplete nutrients and cause side effects. Doxy is a huge depletor of many things. If you want I'll look that up for you. Rocephin (Cefatriaxone) depletes about the same things..so there is not much difference there.