A tape drive assembly (20) for the transmission of data relative to a magnetic storage tape (278) includes a tape head (260), a cartridge receiver (268) and a controller (44). The cartridge receiver (268) selectively receives a cartridge (54) having a lapping tape (478) that laps the tape head (260). The controller (44) dynamically adjusts one of (i) a tension of the lapping tape (478) relative to the tape head (260), (ii) an oscillation frequency of the tape head (260) relative to the lapping tape (478), and (iii) a lateral velocity of the lapping tape (478) relative to the tape head (260). The controller (44) can use an algorithm to adjust these conditions. The algorithm can be based on the pliability of the lapping tape (478), a curvature of the tape head (260) and/or the grit of the lapping tape (478). In addition, or in the alternative, the algorithm can be based on at least one of an output of the tape head (260), a resolution of a signal from the tape head (260), an error rate in reading of data by the tape head (260) from the storage tape (278), an error rate in writing of data by the tape head (260) to the storage tape (278), and a signal-to-noise ratio from the tape head (260).