Lamb-dips of R(0), R(2) and P(2) rovibrational transitions in the (2-0) overtone band of the HD molecule are measured at cryogenic temperatures using the technique of NICE-OHMS spectroscopy. Resulting transition frequencies are 214,905,335,240,(100) kHz for R(0), 219,042,856,794,(150) kHz for R(2) and 206 ,898 ,802,150 ,(150) kHz for P(2). Small, but systematic deviations (at 1.7sigma level) are found from advanced ab initio calculations, supporting results from previous studies probing other lines in the (2-0) band. From a combination difference between the R(0) and P(2) lines, an accurate value for rotational-level spacing in the v=0 ground state is determined, of Delta _{(J=2)-(J=0)}= 8,006,533,168,(26) kHz, well in agreement with theory (at 0.6sigma ). Based on the observation of the dispersive line shape of R(0), the status of proposed models for the elusive line shapes of saturated transitions in HD is discussed.