We examine the internal structure of solar-like stars in detail between 0.8 and 1.4 M and during pre-main-sequence phase. Recent opacity computations of OPAL along with a new hydrodynamical mixing process have been considered. We also introduce up-to-date nuclear reaction rates and explore the impact of accretion, mixing length parameter, nonsolar distributions among metals, and realistic rotation history. Models predict lithium depletion that we compare to the ⁷Li content observations of the Sun and four young clusters of different metallicities and age. We show that we can distinguish two phases in lithium depletion: (1) a rapid nuclear destruction in the T Tauri phase before 20 Myr whatever the mass in our range and largely dependent on the extension and temperature of the convective zone, and (2) a second phase where the destruction is slow and moderate and which is largely dependent on the (magneto)hydrodynamic instability located at the base of the convective zone. Regarding composition we show the interest that takes on helium and above all the mixture of heavy elements: carbon, oxygen, silicium, and iron. We outline the importance of the O/Fe ratio. We note a reasonable agreement on lithium depletion for the two best-known cases, the Sun and the Hyades, for solar-like stars. Other clusters suggest that processes which may partly inhibit the predicted pre-main-sequence depletion cannot be excluded, in particular for stars below ~0.9 M. We finally propose different research areas such as initial stellar models and more realistic atmospheres which could contribute to understanding better this early phase of evolution and which will be the object of subsequent works.