That is the USS Michigan. She carries more than a 150 Tomahawk missiles. They fly much slower and lower than ballistic missiles. USS Lake Erie's missiles could hit them but she would run out of ammunition long before she shot down that submarines entire payload.
USS Michigan is a recycled warship. She was actually built in 1982 and armed with 24 Trident ballistic missiles each with 8 independently targeted reentry warheads. That would be 8 city killing warheads x 24 missiles = a series of unfortunate events.
Some pondering points:
That old battleship's guns could only fire about 175 shells before they burnt out the barrels. That was a badness.
For almost 50 years there was NO way to shoot down incoming ballistic missiles. Wild eyed optimists came up with technical solutions each scary enough to qualify as insane. I don't recall any atmospheric tests involving anybody, navy, army or air force attempting to test a nuclear tipped Terrier, Nike-Hercules or Bomarc against aerial or ballistic missile targets. OTOH, they were pretty insane.
Why did we opt to put a thoroughly tested working anti-ballistic missile on warships instead of somewhere useful? It was a MAD world after all.