Context. More than 100 exoplanets have been discovered around K and G giant stars, and their properties differ considerably from those of the planets found orbiting Sun-like and late-type main-sequence stars. This allows us to study the properties of planetary systems after the host star has evolved off the main-sequence, and it helps us to constrain planetary formation and evolution models. Aims. Our aim is to find out whether the long-period radial velocity variations observed in four giant stars of the Lick survey are caused by orbiting planets, and to study the properties of the planet population as a function of the stellar evolutionary stage. Methods. We analyzed 12 yr of precise radial velocity data for four stars of the Lick sample. In addition, we compared the planet frequency as a function of the evolutionary stage for two surveys, Lick and Express, based on the evolutionary stages derived using Bayesian inference. Results. We report the discovery of two new exoplanets and three exoplanet candidates orbiting giant stars. The best Keplerian fits to the data yield minimum masses of 2.5 MJ and 4.3 MJ for the planets orbiting HD 25723 and 17 Sco, respectively. The minimum masses of an additional candidate around HD 25723, and of planet candidates around 3 Cnc and 44 UMa, would be 1.3 MJ, 20.7 MJ, and 12.1 MJ, respectively. In addition, we compute planet frequencies for the Lick and Express samples as a function of the evolutionary stage. Within each sample, the planet frequency for the horizontal branch stars is the same as for the red giant branch stars. Conclusions. We have discovered two new exoplanets and three new exoplanet candidates, one of them being the second planet in a possible multi-planetary system. Based on our derived planet frequencies, we conclude that stellar evolution does not affect the number of observable planets between the red-giant and horizontal-branch evolutionary stages.