The design for fatigue for offshore wind turbine structures is characterized by uncertainty, resulting from both loading specifications and numerical modelling. At the same time, fatigue is a main design driver for this type of structures. This study presents a strategy to monitor the accumulated fatigue damage in real-time, employing a joint input-state estimation algorithm. Measuring the operational vibrations at well-chosen locations enables the estimation of strain responses at unmeasured locations. The estimation algorithm is applied to a wind turbine on a lattice support structure, for which the response estimates of the lattice members are based on measurements on the turbine tower only. This restriction follows from the difficulty to reliably and robustly measure at locations on the lattice structure. Artificial measurement data is generated with a full-order finite element model, while the strains are estimated with an erroneous reduced-order design model, after inclusion of measurement noise. The strain estimates show that the main frequency content can be captured relatively accurately, except for a small bias and some high frequency disturbance, corresponding to a weakly observable higher mode. This second aspect shows the importance of a trade-off between the accuracy of the reduced-order finite element model and the ill-conditioning of the observability matrix.