Sixty-eight main-sequence members of the Hyades cluster with spectral types ranging from F7 to K1 V have been observed at Li I lambda6707 to determine whether solar-like stars of a given mass, age, and initial composition have a unique surface lithium abundance Li/H. The data are compared with previous Li I observations in the Hyades, and similarities and differences are discussed. For the sample as a whole, the observed distribution of lithium abundances is inconsistent with a unique relationship between lithium abundance and mass. Furthermore, there is strong observational evidence for main-sequence lithium depletion when the data are compared with observations in younger clusters, even for masses that are not predicted to experience such depletion in standard stellar models. Physics not included in standard stellar models is therefore required to explain the lithium abundances of low-mass stars. The degree of dispersion in the Li abundances is a function of mass. The observed dispersion is relatively large in the late F stars (5900-6200 K) and generally small in the G and early K stars. A statistical analysis indicates that an intrinsic dispersion in the lithium abundances of the G stars (5300-5900 K) is present at the 8 sigma confidence level. However, a typical randon B-V error exceeding 0.009m would cause the derived precision to decline below 2 sigma. A second, high-precision (+/- 10 K) relative temperature scale would be desirable for confirming the existence of a lithium abundance dispersion in this temperature range. Among the G stars, vB 9 appears to be highly overdepleted with respect to the trend. Observational errors are substantially larger for the cooler stars, making an analysis of dispersion below 5300 K uncertain. We report a number of detections and upper limits among the coolest stars; the detections may represent the older counterparts to the Li-rich late-type stars seen in the Pleiades. We have discovered two new, short period binaries with lithium abundances well above the mean trend for other stars: BD + 22-degrees 669 and BD + 23-degrees 635. These tidally locked binaries contain the coolest stars in our program, and we report Li i detections for both. We have also confirmed the high lithium abundances previously found for two other tidally locked systems: vB 22 and 62. These results suggest that a star's rotational history affects its surface lithium abundance.