We have determined Li abundances in 55 dwarfs and subgiants that are metal-poor ( - 3.6 < [ Fe/H ] < - 0.7 ) and have extreme orbital kinematics . Our purpose is to examine the Li abundance in the Li-plateau stars and its decrease in low-temperature , low-mass stars . For the stars in our sample we have determined chemical profiles in Stephens & Boesgaard ( 2002 ) . The Li observations are primarily from the echelle spectrograph on the 10 m Keck I telescope with HIRES covering 4700 - 6800 Å with a spectral resolution of \sim 48,000 . The spectra have high signal-to-noise per pixel from 70 to 700 , with a median of 140 . The Li I resonance doublet was detected in 42 of the 55 stars . Temperatures were found spectroscopically by Stephens & Boesgaard ( 2002 ) . Abundances or upper limits were determined for all stars with typical errors of 0.06 dex . Corrections for the deviations from non-local thermodynamical equilibrium for Li in the stellar atmospheres have been made which range from - 0.04 to +0.11 dex . Our 14 dwarf and turn-off stars on the Li plateau with temperatures greater than 5700 K and [ Fe/H ] < - 1.5 give A ( Li ) = log N ( Li ) /N ( H ) + 12.00 of 2.215 \pm 0.110 , consistent with earlier results . We find a dependence of the Li abundance on metallicity as measured by [ Fe/H ] and the Fe-peak elements Cr and Ni , with a slope of \sim 0.18 . We have examined the possible trends of A ( Li ) with the chemical abundances of other elements and find similar dependences of A ( Li ) with the alpha elements , Mg , Ca , and Ti . These slopes are slightly steeper at \sim 0.20 , resulting from an excess in [ \alpha /Fe ] with decreasing [ Fe/H ] . For the n-capture , rare-earth element , Ba , we find a relation between A ( Li ) and [ Ba/H ] which has a shallower slope of \sim 0.13 ; over a range of 2.6 dex in [ Ba/H ] , the Li abundance spans only a factor of two . We have also examined the possible trends of A ( Li ) with the characteristics of the orbits of our halo stars . We find no trends in A ( Li ) with kinematic or dynamic properties . For the stars with temperatures below the Li plateau there are several interesting results . The group of metal-poor stars possess , on average , more Li at a given temperature than metal-rich stars . When we divide the cool stars into smaller subsets with similar metallicities , we find trends of A ( Li ) with temperature for the different metallicity groups . The decrease in A ( Li ) sets in at hotter temperatures for the higher metallicity stars than for the lower metallicity stars . The increased Li depletion in cooler stars could be a result of the increased action of convection since cooler stars have deeper convection zones . This would also make it easier for additional mixing mechanisms , such as those induced by rotation , to have a greater effect in cooler stars . Since the model depth of the convection zone is almost independent of metallicity at a given effective temperature , the apparent metallicity-dependence of the Li depletion in our data may be pointing to subtle but poorly understood mixing effects in low mass halo dwarfs . Predictions for Li depletion from standard and non-standard models seem to underestimate the degree of depletion inferred from the observations of the cool stars .