You can look the specific bonuses up in common/static modifiers...
luck = {
global_trade_power = 0.1 (+10% trade power multiplier)
colonist_placement_chance = 0.05 (+5% colonist chance)
global_missionary_strength = 0.01 (+1% missionary strength)
leader_fire = 1 (+1 leader fire value, still caps at 6)
leader_shock = 1 (+1 leader shock value, still caps at 6)
spy_offence = 0.05 (+5% offensive spying chance)
stability_cost_modifier = -0.10 (-10% stability cost)
defensiveness = 0.1 (+10% defensiveness bonus)
advisor_pool = 1 (1 additional advisor available to choose from when hiring)
free_leader_pool = 1 (1 additional general without costing military points)
heir_chance = 0.25 (25% more likely to get an heir)
global_revolt_risk = -1 (-1% revolt risk in all provinces)
legitimacy = 1 (+1% legitimacy gain per year)
republican_tradition = 0.01 (+1% annual republican tradition gain)
interest = -1 (-1% interest rate on loans)
mercenary_cost = -0.25 (-25% cost for mercenaries)
}
I believe there is also a hidden bonus on ruler stats and chances to get a PU/inheritance but I can't quote it.
Lucky nations in an ironman game are Austria, Castille, England, France, Muscovy, Ottoman Empire, Portugal, and Sweden. If you are playing one of them there is no replacement and you do not get the bonuses. I think the Netherlands can spawn as a lucky nation under certain conditions but I'm not positive about that.
The lucky nations generally tend to perform reasonably well although they generally don't reach their historic heights (for the most part). They are intended to make a late game challenge for the player as well as a more or less recognizable Europe if the player is not involved in Europe. They are far from invincible though.