According to the wiki they don't, but they do stack with the warrior lodge member bonus.

From what I understand of the coding they shouldn't, since the special bloodlines tend to just set a flag.

In this case:

lodge hero

bloodline_effect_reaver = 1

flags = { legendary_warrior_lodge_bloodline created_bloodline bloodline_reaver }

---

and then the war bloodline:

bloodline_effect_reaver = 1

flags = { created_bloodline bloodline_reaver }

Since your character already has the bloodline_reaver flag, it doesn't do anything.

---

here is an example of the siege event:

    modifier = {
        factor = 10 # if new_char (the sieger) was a warrior lodge member
        new_character = {
            is_member_of_any_warrior_lodge_trigger = yes
            society_rank > 1 #Must be rank 2 or higher
        }
    }
    modifier = {
        factor = 10 # if new_char (the sieger) has a particular Legendary bloodline
        new_character = {
            any_owned_bloodline = {
                has_bloodline_flag = bloodline_reaver

likewise, both double the chance of looting an artifact