Yes, primogeniture only really set in after King John's reign.
It was perhaps fortunate for both Lady Lennox and the Duke of Northumberland that she was in Scotland in 1553. For Northumberland, it meant he didn't have to worry about another potential Catholic heiress running about the country - for Margaret, it may well have saved her life. Northumberland's first priority was to capture Mary and Elizabeth, but afterwards, could he have ignored Margaret's closeness to the throne?
Another question is why didn't Mary I, that most Catholic of queens, make her Catholic cousin Margaret - or indeed the latter's son Henry - her successor? Possibly because to do so, she would have had to overturn Henry VIII's 1544 Act of Parliament, on which her own right of succession hinged.