Provided are chimeric or recombinant antibodies (Ab), or antigen binding fragments thereof, or monomeric or dimeric antigen binding proteins, that can specifically bind to human LAG-3 polypeptides, including human LAG-3 polypeptides expressed on the surface of lymphocytes such as activated T cells that have infiltrated tumors or tumor infiltrating lymphocytes (TILs), and methods for making and using them. In alternative embodiments, chimeric or a recombinant antibodies (Ab), or antigen binding fragments thereof, or monomeric or dimeric antigen binding proteins as provided herein are used for in vitro diagnostics, for example, in immuno-histochemistry (IHC), for example, to diagnose and/or treat a cancer, for example, bladder cancer, urothelial carcinoma, breast cancer, lung cancer, Non-Small Cell Lung Cancer, renal carcinoma, Renal Clear cell Carcinoma and/or melanoma or malignant melanoma, by their ability to specifically bind to activated T cells that have infiltrated tumors, or tumor infiltrating lymphocytes.