We present data for four ultra-Li-deficient, warm, halo stars. The Li defic
iency of two of these is a new discovery. Three of the four stars have effe
ctive temperatures T-eff similar to 6300 K, in contrast to previously known
Li-deficient halo stars, which spanned the temperature range of the Spite
plateau. In this paper we propose that these and previously known ultra-Li-
deficient halo stars may have had their surface lithium abundances reduced
by the same mechanism as produces halo field blue stragglers. Even though t
hese stars have yet to reveal themselves as blue stragglers, they might be
regarded as "blue-stragglers-to-be" In our proposed scenario, the surface a
bundance of Li in these stars could be destroyed (1) during the normal pre-
main-sequence single-star evolution of their low-mass precursors, (2) durin
g the post-main-sequence evolution of an evolved mass donor, and/or (3) via
mixing during a mass-transfer event or stellar merger. The warmest Li-defi
cient stars at the turnoff would be regarded as emerging "canonical" blue s
tragglers, whereas cooler ones represent sub-turnoff-mass blue-stragglers-t
o-be. The latter are presently hidden on the main sequence, Li depletion be
ing possibly the clearest signature of their past history and future signif
icance. Eventually, the main-sequence turnoff will reach down to their mass
, exposing those Li-depleted stars as canonical blue stragglers when normal
stars of that mass evolve away. Arguing against this unified view is the o
bservation that the three Li-depleted stars at T-eff similar or equal to 63
00 K are all binaries, whereas very few of the cooler systems show evidence
for binarity; it is thus possible that two separate mechanisms are respons
ible for the production of Li-deficient main-sequence halo stars.