There's a guy in my racing club who started racing in the 55+ age group. He's since won a medal at nationals. You're probably too old to go pro because even for the genetic outliers who make it as a pro it takes years to build up the endurance that lets them train as much as pros need to train. But you're not too old to be a successful amateur.
Running doesn't make you faster on the bike, although sometimes former runners make good racers. But that's because they already have an aerobic engine.
Road racing is an aerobic sport. Weight lifting can help if you are unusually weak, and strengthening your core can help. But generally weight lifting is not that useful.
I suggest you buy a good book on training (i.e. Friel's "training bible") and read it.