Litigate rhymes with:
profligate, abrogate, applegate, arrogate, bathgate, bishopsgate, castigate, congregate, corrugate, delegate, desegregate, digate, filegate, floodgate, fumigate, holgate, instigate, interrogate, investigate, irangate, iraqgate, irrigate, koreagate, mastergate, mitigate, navigate, northgate, obligate, profligate, propagate, relegate, seagate, segregate, southgate, stargate, subjugate, tailgate, travelgate, watergate, westgate, wingate
Litigate sounds like:
latched, latest, liddicoat, litigated, lodged, loudest