We have studied the evolution of the structural properties as well as the static and dynamic spin correlations of spin ice Ho2Ti2O7, where Ho was partially replaced by non-magnetic La. The crystal structure of diluted samples Ho2-xLaxTi2O7 was characterized by x-ray and neutron diffraction and by Ho L-III-edge and Ti K-edge extended x-ray absorption fine structure (EXAFS) measurements. It is found that the pyrochlore structure remains intact until about x = 0.3, but a systematic increase in local disorder with increasing La concentration is observed in the EXAFS data, especially from the Ti K edge.Quasi-elastic neutron scattering and ac susceptibility measurements show that, in x<= 0.4 samples at temperatures above macroscopic freezing, the spin -spin correlations are short ranged and dynamic in nature. The main difference with pure spin ice in the dynamics is the appearance of a second, faster, relaxation process.