We report on cyclotron frequency measurements on trapped 206,207Pb+ ions by means of the non-destructive Fourier-transform ion-cyclotron-resonance technique at room temperature. In a proof-of-principle experiment using a quartz crystal instead of a coil as a resonator, we have alternately carried out cyclotron frequency measurements for 206Pb+ and 207Pb+ with the sideband coupling method to obtain 21 cyclotron-frequency ratios with a statistical uncertainty of 6 × 10-7. The mean frequency ratio R¯ deviates by about 2σ from the value deduced from the masses reported in the latest Atomic Mass Evaluation. We anticipate that this shift is due to the ion-ion interaction between the simultaneously trapped ions (≈100) and will decrease to a negligible level once we reach single-ion sensitivity. The compactness of such a crystal makes this approach promising for direct Penning-trap mass measurements on heavy and superheavy elements.