Inspired by the recent conjecture originated from graduated dark energy that the Universe has recently transitioned from anti-de Sitter vacua to de Sitter vacua, we extend the standard Lambda CDM model by a cosmological constant (Lambda(s)) that switches sign at a certain redshift z(dagger), and we call this model Lambda sCDM. We discuss the construction and theoretical features of this model in detail and find out that, when the consistency of the Lambda sCDM model with the cosmic microwave background (CMB) data is ensured, (i) z(dagger) greater than or similar to 1.1 is implied by the condition that the Universe monotonically expands, (ii) H-0 and M-B (type Ia supernovae absolute magnitude) values are inversely correlated with z(dagger) and reach H-0 approximate to 74.5 km s(-1) Mpc(-1) and M-B approximate to -19.2 mag for z(dagger) = 1.5, in agreement with the SHOES measurements, and (iii) H(z) presents an excellent fit to the Ly-alpha measurements provided that z(dagger) less than or similar to 2.34. We further investigate the model constraints by using the full Planck CMB data set, with and without baryon acoustic oscillation (BAO) data. We find that the CMB data alone does not constrain z(dagger), but the CMB + BAO data set favors the sign switch of Lambda(s), providing the constraint z(dagger )= 2.44 +/- 0.29 (68% C.L.). Our analysis reveals that the lower and upper limits of z(dagger) are controlled by the Galaxy and Ly-alpha BAO measurements, respectively, and the larger z(dagger) values imposed by the Galaxy BAO data prevent the model from achieving the highest local H-0 measurements. In general, the Lambda sCDM model (i) relaxes the H-0 tension while being fully consistent with the tip of the red giant branch measurements, (ii) relaxes the M-B tension, (iii) removes the discrepancy with the Ly-alpha measurements, (iv) relaxes the S-8 tension, and (v) finds a better agreement with the big bang nucleosynthesis constraints on the physical baryon density. We find no strong statistical evidence to discriminate between the Lambda sCDM and Lambda CDM models. However, interesting and promising features of the Lambda sCDM model, which we describe in our study, provide an advantage over Lambda CDM.