Could a infection in the lower spine cause weakness in the psoas muscle? how do you strength it if so?

Potentially: An infection of the spine or the paraspinal area could definitely affect your psoas muscles. This would usually be accompanied by other signs of infection (fever, etc.). Conditions associated with spinal infections include chronic immunosuppression, IV drug abuse, and prior spinal surgery. If you suspect you might have a spinal infection, you should definitely see your doctor asap.