A new methodology for assessing linear energy transfer (LET) and relative biological effectiveness (RBE) in proton therapy beams using thermoluminescent detectors is presented. The method is based on the different LET response of two different lithium fluoride thermoluminescent detectors (LiF:Mg,Ti and LiF:Mg,Cu,P) for measuring charged particles. The relative efficiency of the two detector types was predicted using the recently developed Microdosimetric d(z) Model in combination with the Monte Carlo code PHITS. Afterwards, the calculated ratio of the expected response of the two detector types was correlated with the fluence- and dose- mean values of the unrestricted proton LET. Using the obtained proton dose mean LET as input, the RBE was assessed using a phenomenological biophysical model of cell survival. The aforementioned methodology was benchmarked by exposing the detectors at different depths within the spread out Bragg peak (SOBP) of a clinical proton beam at iThemba LABS. The assessed LET values were found to be in good agreement with the results of radiation transport computer simulations performed using the Monte Carlo code GEANT4. Furthermore, the estimated RBE values were compared with the RBE values experimentally determined by performing colony survival measurements with Chinese Hamster Ovary (CHO) cells during the same experimental run. A very good agreement was found between the results of the proposed methodology and the results of the in vitro study.