We explore the electrical transport and magneto-conductance in quasi two-dimensional strongly correlated ultrathin films of LaNiO$_{3}$ (LNO) to investigate the effect of hetero-epitaxial strain on electron-electron and electron-lattice interactions from the low to intermediate temperature range (2K$sim$170K). The fully epitaxial 10 unit cell thick films spanning tensile strain up to $sim4%$ are used to investigate effects of enhanced carrier localization driven by a combination of weak localization and electron-electron interactions at low temperatures. The magneto-conductance data shows the importance of the increased contribution of weak localization to low temperature quantum corrections. The obtained results demonstrate that with increasing tensile strain and reduced temperature the quantum confined LNO system gradually evolves from the Mott into the Mott-Anderson regime.