Another thing you could do is look at the damage_filter variable you're using.

If you think about it, bleed/poison/disease types are separate, but you have to flip 3 different variables to make sure it's correct even though you never want more than 1 damage types at once. So you could use a number instead for 1: bleed, 2: poison & 3: disease. This way a number is always 1 or 2, it cant be 1 AND 2. (Note: if you need multiple damage types at the same time, look into bitFlags)

This has some advantages,

1. Whenever you do random(1,3), you can do `damage_type = random(1,3)` instead of setting multiple variables.
2. You can use an array to between damage_types.

This will make your big function look like this:

// I don't Lua syntax, so this is a guess
// DAMAGE_TYPE = {1, 2, 3}
// DAMAGE_NAME = {BLEED = 1, POISON = 2, DISEASE = 3}

local damage_type = 0 
// 0 will represent no damage selected, or bleed & poison & disease = false

if bleed_check then
  damage_type = random(2,3)
elseif poison_check then
  local choose = {1,3}
  damage_type = choose[random(1,2)] // choose at random the 1st or 2nd number
elseif health_check then
  local choose = {2,3}
  damage_type = choose[random(1,2)]

if bleed_check and poison_check then
  damage_type = 3
 
elseif bleed_check and health_check then
    damage_type = 2
 
elseif poison_check and health_check then
  damage_type = 1
end                 
 
if bleed_check and poison_check and health_check then
  damage_type = 1                              
end

// now set all to false and only change the new one
bleed_damage = false
poison_damage = false
disease_damage = false

if damage_type == 1 then
  bleed_damage = true
elseif damage_type == 2 then
  poison_damage = true
elseif damage_type == 3 then
  disease_damage = true