
President Ronald Reagan appointed Baylson as the United States Attorney for the Eastern District of Pennsylvania in 1988. He held on to that position until 1993. Baylson then returned to private practice, where he served as a partner with Duane Morris until 2002. President George W. Bush nominated Baylson to a seat on the Eastern District Court on January 23, 2002. On April 30, 2002, the United States Senate confirmed the judge and he received his commission on June 19.
Baylson is a member of the Advisory Committee on Civil Rules of the Committee on Rules of Practice and Procedure of the Judicial Conference of the United States. He currently is an Adjunct Professor at Temple University Beasley School of Law and the University of Pennsylvania Law School. Baylson was a founder of Gaudenzia, Inc., and would later counsel the company, which is the largest non-profit provider of alcohol, drug and mental health rehabilitation services in Pennsylvania.
According to an ABA Journal article, "Federal judge suspends transplant rules in case of dying girl," on Thursday, June 6 2013, U.S. District Judge Baylson decided to temporarily suspend transplant rules in the case of Sarah Murnaghan. She is a ten-year-old girl who suffers from cystic fibrosis. If she doesn't get new lungs she could die. Baylson's judgment permitted a ten-day temporary restraining order (PDF), which suspended rules that put kids under twelve years of age at the bottom of the waiting list to receive adult lung transplants. Kids also have to wait to receive pediatric lungs, which are not donated often.
According to a column, "Judge Rules Sarah Murnaghan Can Be On Adult Lung Transplant List," statistics obtained from the Organ Procurement and Transplantation Network (OPTN) revealed that in 2012, ten lung transplants were given to kids who were ten or younger. After Baylson considered the medical severity of Murnaghan's condition, he grated the motion for the girl, so she could be a recipient of donated lungs from adults. The judge also compared Murnaghan's condition to the medical severity of individuals who were over twelve years old in the OPTN system before he made his June 6 ruling. Baylson stated, "This Order shall remain in effect unless and until the Court orders otherwise at the conclusion of the hearing on a preliminary injunction. A hearing on the preliminary injunction will be held June 14, 2013, at 10 a.m. in Courtroom 3A."
The ABA article quoted Murnaghan's mother, Janet Murnaghan, when she said, "We are beyond thrilled. Obviously we still need a match."