We present data for four ultra-Li-deficient, warm, halo stars. The Li deficiency of two of these is a new discovery. Three of the four stars have effective temperatures Teff ~ 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 these stars have yet to reveal themselves as blue stragglers, they might be regarded as "blue-stragglers-to-be." In our proposed scenario, the surface abundance of Li in these stars could be destroyed (1) during the normal pre-main-sequence single-star evolution of their low-mass precursors, (2) during 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-deficient stars at the turnoff would be regarded as emerging "canonical" blue stragglers, whereas cooler ones represent sub-turnoff-mass blue-stragglers-to-be. The latter are presently hidden on the main sequence, Li depletion being possibly the clearest signature of their past history and future significance. 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 observation that the three Li-depleted stars at Teff ≃ 6300 K are all binaries, whereas very few of the cooler systems show evidence for binarity; it is thus possible that two separate mechanisms are responsible for the production of Li-deficient main-sequence halo stars.