If my dad died 3 years ago in part because of what I believe to be medical mistakes, is it too late to pursue a lawsuit?

It  likely depends on whether or not you knew or should have known about the medical mistakes.

The medical malpractice statute of limitations is found in Utah Code § 78B-3-404 (http://le.utah.gov/code/TITLE78B/htm/78B03_040400.htm/).  In relevant part, it states as follows:

• (1) A malpractice action against a health care provider shall be commenced within two years after the plaintiff or patient discovers, or through the use of reasonable diligence should have discovered the injury, whichever first occurs, but not to exceed four years after the date of the alleged act, omission, neglect, or occurrence.

              (2) Notwithstanding Subsection (1):

              (a) in an action where the allegation against the health care provider is that a foreign object has been wrongfully left within a patient's body, the claim shall be barred unless commenced within one year after the plaintiff or patient discovers, or through the use of reasonable diligence should have discovered, the existence of the foreign object wrongfully left in the patient's body, whichever first occurs; or

              (b) in an action where it is alleged that a patient has been prevented from discovering misconduct on the part of a health care provider because that health care provider has affirmatively acted to fraudulently conceal the alleged misconduct, the claim shall be barred unless commenced within one year after the plaintiff or patient discovers, or through the use of reasonable diligence, should have discovered the fraudulent concealment, whichever first occurs.