Lithium fluoride thermoluminescent radiation detectors with different dopant concentrations (7LiF:Mg,Ti and 7LiF:Mg,Cu,P) were exposed to 1H and 4He ions at the Heavy Ion Medical Accelerator in Chiba (HIMAC) in order to investigate their response to energetic light charged particles. Computer simulations with the Monte Carlo code PHITS were performed for a better interpretation of the experimental data. The results were compared with literature efficiency data and with the results of a recently developed microdosimetric efficiency model. In case of the main peak signal of 7LiF:Mg,Ti detectors, the determined efficiency values are in good agreement with previous investigations. Discrepancies in the efficiency of high temperature signal due to well-known non-linearity effects are reported. For 7LiF:Mg,Cu,P detectors, an anomalous thermoluminescence behavior in the low temperature part of the signal was found and discussed. Depending on the light quantification process, differences up to 30% in the dose assessment can be obtained, affecting also the relative efficiency determination process. An explanation of this phenomenon as a consequence of local migration of the charged carriers between the low temperature peaks and the main peak is presented. The implications of these findings on the use of LiF:Mg,Cu,P detectors in radiation environments characterized by the presence of 1H and 4He ions (i.e. space and proton therapy) are discussed. In order to avoid the occurrence of this anomalous behavior, it is advised to preheat the detectors after energetic light particle exposures.