How do I remedy a ledger board that is pulling away from the house?
Even if you've restrained the deck to prevent the ledger from pulling away more, I would be worried about those nails failing. If there's much separation between the ledger and the house you'll be putting bending stress on those nails. Is it feasible to add the lag bolts now? You haven't provided a picture or much description of the ledger area so it's hard to say what's practical, but I would say that getting that ledger securely fastened is critical to the safety of the deck.

Since this deck seems like it might have been a casual DIY job, you might also investigate the water membranes / flashing to make sure you're keeping moisture away from the house. Flashing may be difficult to retrofit but if it's missing or inadequate you should make an attempt to address that problem. Water can cause a huge amount of damage to both the deck and the house. There are several questions on this site that discuss ledger flashing.

If you can't properly secure the ledger to the house you might consider converting the porch to be free-standing, but that's a whole new project.