early 15c., from Late Latin dilapidationem (nominative dilapidatio) "a squandering," noun of action from past participle stem of Latin dilapidare "throw away, squander, waste," literally "pelt with stones" (thus "ruin, destroy") or else "scatter like stones," from dis- "asunder" (see dis-) + lapidare "throw stones at," from lapis (genitive lapidis) "stone." "Taken in Eng. in a more literal sense than was usual in Latin" [OED].
1560s, "to bring a building to ruin," from Latin dilapidatus, past participle of dilapidare "to squander, waste," originally "to throw stones, scatter like stones;" see dilapidation. Perhaps the English word is a back-formation from dilapidation.