Yeah, pulling out a lag bolt like that will make an even bigger mess of the tire. I got one like that ^^^^^ in a rear wheel about 5 years ago. As usual, I was carrying a Leatherman tool, so I could unscrew it and minimize damage to the tire casing. Spare tube and a dollar bill got me to my destination and then home. Patched the tube, retired the tire.

Note to self - cut up an old tyvek envelope and put bits in every seat bag....