Saving Lives, Saving Costs Act This bill establishes a framework for health care liability lawsuits to undergo review by independent medical review panels if health care professionals (practicing physicians or their agents or employees), providers, or organizations allege adherence to clinical practice guidelines. The Department of Health and Human Services (HHS) must publish clinical practice guidelines provided and maintained by national or state medical societies or medical specialty societies designated by HHS. HHS must ensure that guidelines are developed in accordance with certain standards, including standards related to transparency, the composition of the panel, and the review of existing evidence. Professional organizations and participants in guideline development may not be held liable for injury allegedly caused by adherence to a guideline to which they contributed. The bill does not preempt: (1) any state or federal law that imposes greater procedural or substantive protections for health care providers and health care organizations from liability, loss, or damages than those provided under this bill; (2) any state or federal law that creates a cause of action; or (3) any defenses otherwise available. The bill gives district courts jurisdiction over health care liability actions against health care professionals, providers, or organizations practicing within clinical practice guidelines. Defendants may remove health care liability actions brought in a state court to a district court.