2013 LEXUS GS Engine Problems

I started my car in the morning and when I started the engine it was an instant extreme rough idle with the engine light and traction control light blinking on my dashboard and the engine cuts out on its own. I have my car at a Toyota dealership since it’s closer than the Lexus dealership and they have ran an extensive testing diagnostic on my car resulting in a valve stuck open and a valve spring fell out. I have kept up the regular maintenance on my car, like every 5,000 miles fully synthetic oil changes, premium gas, regularly checking for recalls, always checking my fluids, correct tires and tire pressure, and I have in no way misused my car since it’s the only car I have to drive. I found that Lexus had a recall on the GS 350 for the 2007 to 2011 years for the problem I’m...