Strong spin-orbit coupling (SOC) in combination with a lack of inversion symmetry and exchange magnetic interaction proves to be a sophisticated instrument allowing efficient control of the spin orientation, energy and trajectories of two-dimensional (2D) electrons and holes trapped at surfaces or interfaces. Exploiting Kondo-related phenomena and crystal-electric-field effects at reduced dimensionalities opens new opportunities to handle their spin-dependent properties offering novel functionalities. We consider here a 2D Kondo lattice represented by a Si-Ir-Si-Yb (SISY) surface block of the heavy-fermion material YbIr2Si2. We show that the Kondo interaction with 4f moments allows finely tuning the group velocities of the strongly spin-polarized carriers in 2D itinerant states of this noncentrosymmetric system. To unveil the peculiarities of this interaction, we used angle-resolved photoemission measurements complemented by first-principles calculations. We established that the strong SOC of the Ir atoms induces spin polarization of the 2D states in SISY block, while the 2D lattice of Yb 4f moments acts as a source for coherent f-d interplay. The strong SOC and lack of inversion symmetry turn out to lead not only to the anticipated Rashba-like splitting of the 2D states, but also to spin splitting of the 4f Kramers doublets. They couple temperature-dependently to the spin-polarized 2D states and thereby guide the properties of the latter.