Lotteries rhymes with:
arteries, batteries, directories, documentaries, eateries, factories, factory's, histories, history's, mysteries, refractories, victories
Lotteries sounds like:
ladders, laterza, lathers, lathouris, latter's, leader's, leaders, leaders', leadwork, leathers, leatrice, lehder's, lethargic, lethargy, letters, literacy, liters, litters, liturgy, loaders, lodwrick, looters, lueders