In the registers I find two more James Price, both born in 1816 in Scotland, in St Angus and Dundee. If you include all James Prices that figure in Scotland census, 1841, there about 20. None born in Lisbon. One of them lived in Stirlingshire too, born in 1791, he could be the father of the James Price born in 1815.
At that time children were registered in the parrish, for catolics. If he was protestant he probably was registered in British Church. I checked familysearch site, based on mormons archives, usually they have all register from british chapels, at least in Portugal. Maybe he was born on board some british ship returning to Scotland, by 1815 there was an heavy traffic, as Napoleonic wars were just ending. I could try to check Lisbon Archives online, but I must know the exact parrish where he was baptized, if he was a catholic. Its impossible to check all register books, they are too many. . I would suggest that you search Airth or Stirlingshire archives, if they exist.