How could I gain lawful permanent residence with entry without inspection?

That can get complicated. If you enter without inspection, then you are 'usually' disqualified from becoming a lawful permanent resident green card holder 'unless' you trigger a ten year ban on immigration, wait or somehow manage to qualify and seek a waiver, and process at a U. S. Embassy or Consulate. There are a few unusual situations that may not require a waiver. There are limited situation, where a person who was petitioned by April 30, 2015, directly or indirectly, may be able to pay a penalty and 'file to process' in the U. S. I strongly recommend an appointment with a competent and experienced immigration attorney, who can investigate and provide legal advice before more complications take place.