The CD57 test (only from Labcorp) measures a subset of NKT cells. These are Natural Killer T Cells. These T cells are actors in the innate immune response. In other words, these cells automatically attack what our immune system sees as foreign invaders. Our immune systems are naturally smart (anthropomorphically). They have pattern recognition cells which can determine tissues/cells that belong in our bodies from things (like bacteria) that do not belong in our bodies. The second part of the immune system, the acquired immune system relates to a complex set of reactions by which the immune system learns to make specific antibodies to attack the foreign invader. In some situations only the innate immune system is in play. Primarily this occurs when the "invaders" are intracellular. The acquired responses just don't work here. In the case of Lyme disease it is the intracellula- L-forms which are attacked by the NKT cells. When the CD57 count is low it would appear these cells are busy combating the L-forms of Lyme. Unfortunately, the innate immune system is never 100% effective in eliminating the bacteria. This is one of the mechanisms by which Lyme is able to persist in the face of antibiotics and immune responses.
C3a and C4a (Labcorp) are products of the complement system, cleaved from C3 and C4. These proteins are mobilized by the immune system as part of its acquired and to a lesser extent innate immune responses. These proteins can attach to unwanted bacteria and target them for destruction. These tests are sensitive indicators of a busy immune system attacking unwanted proteins or germs. These markers can provide a general sense of immune activation in the face of infection or inflammation.
C3d (Quest only) is a test for circulating immune complexes (CIC). These antibody/antigen complexes are not supposed to be present in our blood. The presence of these CICs indicates infection or inflammation and can be used as another indicator of disease activity.
C-reactive protein (CRP) is a naturally occurring protein found in blood circulation. It is one of two proteins which activate the complement system associated with immune activation. This is another marker which can help assess disease activity. This marker is elevated in many diseases and is not specific for Lyme disease. When used here, the clincially useful cut-off points may be much lower than the "normal" reported by the lab.
There are many other labs/markers of infection/inflammation. But here a few that seem to confuse many patients (and doctors).