Leasowe lighthouse to where the rally is is about 3.5 to 4 miles, so you could carry on to Seacombe Ferry which is another 2.5 miles. Giving you an out and back trip of 12 miles or so. The prom is almost totally flat apart from one small gravelly/sandy hill when you get to Leasowe foreshore. It wouldn’t be much fun on a road bike, but it’s still doable.
Or as the previous poster said, if you’re staying in Liverpool come over on the ferry, ride to New Brighton and watch the rally for a bit and carry on to Leasowe or Meols. There’s a pirate ship built from driftwood at Egremont and you can get ice creams and a meal in New Brighton.