There are several synonyms to express "by ill luck." The phrase "unfortunately" is a commonly used synonym. It means "regrettably" or "sadly." Another option is "unluckily," which suggests that an unfavorable event has taken place in one's life. "Miserably" and "wretchedly" are other words that can be used as synonyms to describe a situation where things have gone wrong. "Inopportunely" can also be used, as it implies that the timing of the event could not have been worse. Finally, "catastrophically" is a more dramatic way of expressing "by ill luck" and often describes an event which has potentially disastrous consequences.