The star formation history (SFH) and the properties of the dwarf galaxy LGS 3 are analyzed using color-magnitude (CM) diagrams plotted from VRI photometry of 736 stars. The distance to the galaxy is estimated through the position of the tip or the red giant branch. Two acceptable results have been obtained: 0.77+/- 0.07 Mpc and 0.96+/- 0.07 Mpc, although the first value is favored by complementary considerations on the stellar content of the galaxy. Both values make LGS 3 a possible satellite of M31 or of M33. The SFH is investigated for each of the two adopted distances comparing the observed (CM) diagrams with model CM diagrams computed for different star formation rates (psi (t)) and chemical enrichment laws (Z(t)). The results are compatible with LGS 3 having been forming stars since an early epoch, 15-12 Gyr ago, at an almost constant rate if distance is 0.77 Mpc or at an exponentially decreasing rate if distance is 0.96 Mpc. According to our models, the current metallicity would range from Z =~ 0.0007 to Z =~ 0.002. Other results are the current psi (t): (0.55+/- 0.04)x 10(-10) M_sun yr(-1) pc(-2) or (0.47+/- 0.07)x 10(-10) M_sun yr(-1) pc(-2) , depending of the distance, and its average for the entire life of the galaxy, bar psi =(1.4+/- 0.1)x 10(-10) M_sun yr(-1) pc(-2) . At the present psi (t), the probability of LGS 3 having an HII region is 0.2, which is compatible with the fact that no HII regions have been found in the galaxy. Its fraction of gas relative to the mass intervening in the chemical evolution is about 0.40 and its percentage of dark matter (that which cannot be explained as stellar remnants or by extrapolation of the used IMF to low masses) is 95%. The results for psi (t) and Z(t) for d=0.77 Mpc are compatible with a moderate outflow of well mixed material (lambda =3), but large outflow rate (lambda =30) is required to account for the results for d=0.96 Mpc. The latter would imply that, if the amount of dark mass associated to the galaxy is constant, the initial dark matter fraction was about 50%. In both cases, a large fraction of freshly made metals (gamma =0.85 for the case of d=0.77 Mpc and gamma =0.36 for d=0.96 Mpc) should also escape from the galaxy before mixing with the interstellar medium to make the results compatible with the theoretical yields. LGS 3 is considered an intermediate type between dIr and dE. However we find that it shows characteristics typical of dIrs (the M_gas/L_B ratio and the SFH shape), the main difference being that its mass and star formation rate (present and averaged) are one to two orders of magnitude smaller than those of other dIrs. This makes the absence of HII regions a simple probabilistic effect. Considering this and the fact that LGS 3 can continue to form stars for a further 10 Gyr at a rate equal to that averaged for its past history, we conclude that this galaxy may be considered just a dIr in the tail of the distributions of mass, luminosity and star formation rate.