I’m thinking of cutting back about 1/3 of these vertical branches each year for the next 3 years to about 6” above the ground. Is that the correct approach to managing this Lilac? Is this the correct time to do the first cutting?
In general, flowering shrubs are pruned after bloom is complete. Perhaps the most common practice is to remove a third of the stems to the ground each year. An alternate method is to periodically cut everything to just above the soil. With the latter method, bloom may not return until the second year.
See “Pruning Large, Overgrown Lilacs” (https://hortnews.extension.iastate.edu/1993/2-10-1993/lilac.html) and “Prune lilacs soon after bloom” (http://extension.oregonstate.edu/gardening/prune-lilacs-soon-after-bloom).
In your case, I would begin by removing the low stem toward the right which blocks the pathway. Next, I would remove all growth which touches the house.