We report ^{7}Li-NMR studies on LiInCr_{4}O_{8} and LiGaCr_{4}O_{8}, in which Cr^{3+} ions with spin 3/2 form a breathing pyrochlore lattice, a network of tetrahedra with alternating sizes. In LiInCr_{4}O_{8} with large alternation, the nuclear relaxation rate 1/T_{1} shows an activated temperature (T) dependence down to 18 K, indicating a singlet ground state with a spin gap. This behavior, however, is disrupted by an antiferromagnetic transition at 13 K, which is preceded by another, most likely structural, transition at 16 K. In contrast, LiGaCr_{4}O_{8} with a small alternation shows no spin gap but exhibits a first-order antiferromagnetic transition over a distributed T range 13-20 K. Nevertheless, 1/T_{1} of the paramagnetic phase diverges toward 13 K, indicating proximity to a second-order transition. The results indicate that LiGaCr_{4}O_{8} is located in the vicinity of a tricritical point in the phase diagram.
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