We have recently proposed a varying cosmological constant model for which we now test our proposal with the use of two large collections of observational Gold data of supernovae Type Ia (SNe Ia) and HII Galaxies (HIIGx) data as standard candles for constructing the Hubble diagram at redshifts beyond the current reach of Type Ia supernovae. For this aim, we obtain the luminosity distances from the proposed varying. models which have been briefly summarized. Using these luminosity distance values, we present the modulus values from which we test the accuracy of the models by probing the Gold data and HII Data confirming that the relation between the emission-line luminosity and ionized-gas velocity dispersion is a reliable modulus indicator. From the chi(2) minimization and the maximization of the likelihood function, we optimize the cosmological parameters in each cosmological model. While the best model is obtained as the Lambda CDM for Gold data, our model with a Lambda depending on the matter density rho is obtained as the best model for HII data. Moreover, the statistical tools, such as the Akaike (AIC), and Bayes (BIC) Information Criteria favor the standard Lambda CDM model over our Lambda proportional to rho model with a relative BIC of 372/383 for Gold data, but same criteria favor our Lambda proportional to rho model over Lambda CDM with 1055/1120 for HII Galaxy data. We also test the accuracy of our models by comparison of the theoretical and observational modulus values for both data, and illustrate the Hubble diagrams for all varying Lambda models showing a worse fit with respect to Lambda CDM model for Gold Data, and a best fit with Lambda proportional to rho model for HII Data, through given statistical confidence tables. (C) 2019 Elsevier B.V. All rights reserved.