Lying on a visa application is a fraud against the U.S. government that triggers inadmissibility and ineligibility for a visa. And, since you lied about the crime in question, you must have at least suspected that the crime itself would have negative immigration consequences. You were right. However, by lying on the application you compounded your troubles and now have two issues to overcome instead of just the original crime.
A formal court conviction for a crime is not necessary for the immigration authorities to deem you inadmissible (ineligible for a visa or green card) based on the crime or your having made a misrepresentation about the crime on a visa or green card application. Immigration laws treat lying on an application for immigration benefits as a crime involving moral turpitude. Your only recourse will most likely be to convince the U.S. government to forgive or overlook the misrepresentation, by applying for what's called a "waiver of inadmissibility." The type of waiver you need depends on whether you are seeking to enter the U.S. as a permanent resident (an immigrant) or temporarily (a nonimmigrant), such as for employment.
Nonimmigrant visa applicants must request a waiver of inadmissibility from the U.S. consulate abroad. There is no specific form to be filed for the nonimmigrant waiver. Upon submitting your application for a visa an interview will be scheduled for you and a consular officer will decide whether or not to recommend to the Department of Homeland Security (DHS) to grant the waiver. In making that decision, the officer will consider the following, among other factors:
If the consular officer does not make a favorable recommendation to the DHS, your nonimmigrant visa application may be denied. NOTE: K-visa, T-visa, and U-visa nonimmigrant applicants as well as those applying for Temporary Protected Status (TPS) must file for an immigrant waiver.
The immigrant waiver application is filed on USCIS Form I-601, Application for Waiver of Grounds of Inadmissibility.The waiver does not require a consular recommendation but remains discretionary, meaning the immigration authorities can make a subjective judgment about whether to grant it or not.
The criteria for I-601 waivers are also must stricter than for nonimmigrant waivers, simply because granted the waiver would allows the person's subsequent adjustment of status to permanent U.S. resident. There are criteria you must meet for a waiver of the misrepresentation and for the crime itself. However, some crimes, by law, cannot be waived.
Crimes that will render you forever barred from entering the U.S., with no available waivers, are:
In the case of other crimes, you may qualify for a waiver if you have a qualifying relative in the U.S., i.e., a spouse, child, or fiancé who is also a U.S. citizen (USC) or a lawful permanent resident (LPR) of the U.S. and either:
To qualify for a waiver for the misrepresentation on your visa application, you must again have a qualifying relative in the U.S. as well as demonstrate that the qualifying relative will face extreme hardship if the waiver is not granted.
Any time a family is separated, hardships, such as financial hardship associated with the separation itself, are expected. Therefore, those hardships alone are usually not sufficient to meet the extreme standard. And again, only hardship to the qualifying family member is considered. On the contrary, all negative factors relating to you will be considered and weighed against the favorable hardship factors, such as:
In a nutshell, while the U.S. government attempts to protect qualifying relatives in the U.S. from hardship that is extreme, it also has the duty of safeguarding society as a whole. You can learn more about what factors constitute extreme hardship in the article, "Extreme Hardship" Waivers Following an Immigrant Visa Denial.
It is not possible to predict the outcome of your case without an in-depth analysis of the facts surrounding your individual situation. The chances of denial are very high. You are strongly urged to consult with an experienced immigration attorney to discuss your situation in depth before filing your application.