It's good that they are following up your suggestion of lupus. This is certainly worthwhile exploring and I have read numerous accounts of people whose low white cell count was the first sign of lupus and who were sent for oncological investigation because of it. I have no idea how often a low white blood count is accompanied by abnormalities in the "lupus anticoagulant" test
The tests for the presence of " lupus anticoagulant " are the clotting tests mentioned by Raglet. They can show the presence of antibodies called antiphospholipids.These antibodies were first identified in people with lupus but they can be present in people without lupus. The term anticoagulant is misleading because although in the test tube clotting times are slower than normal seeming to indicate a risk of bleeding, in human bodies they can indicate a tendency to clot formation.
The link in the lupus context between the presence of anti phospholipid antibodies and low white blood cell counts is that they are both criteria for a lupus diagnosis so long as there are other signs and symptoms of lupus.
See the ACR criteria list.
The presence of these antibodies does not necessarily mean there will be a clotting episode. The statistic usually given is that one third of people with lupus have these antibodies but only one third of those will ever suffer any problems from them. The lupus anti coagulant testing should be accompanied by tests for anticardiolipins, another sort of antiphospholipid antibody. Either can be abnormal at different times. They can come and go as part of the normal workings of the immune system. They are not always autoimmune either: levels can be abnormal due to infections for example such as Lyme disease or HIV/AIDS.
A false positive syphilis test can be another indication.
There are additional tests to show if the antibodies are autoimmune, or if other sorts of clotting abnormalities or another disease is causing them.
Bye for now