What kind of arthritis is caused by Lyme disease?

Specific. It is specific to Lyme disease is called Lyme Disease arthritis. It is not rheumatoid or osteoarthritis.
Inflammatory. Lyme disease causes arthritis in less than 9% of patients, usually within weeks to months after a tick bite and skin manifestations, and usually in untreated patients. It is considered a late manifestation and most commonly affects large joints such as knees, but can affect any and the joint is swollen, painful, warm and sometimes red. Treatment is with Amoxicillin or cephtriaxone.