I would talk with whoever your GM will be. If you don't want the tail to do anything in particular you could just describe your character has having a tail. Rakshasa or Serpentine Bloodlines could be thematically appropriate and give reason why you might have a tail.
Metamorph alchemist will let you turn into monstrous humanoids for long periods of time starting at 5th level. As lamia are monstrous humanoids you could turn into one at 9th level when u get the ability to turn into large monstrous humanoids with this archetype if that’s your thing.
The salamander bloodline only allows you to have a tail for short periods of time. The spell Monstrous Physique II allows you to turn into a large monstrous humanoid. The spell has the same duration as the bloodline ability, but cannot be broken up and used multiple times per day. The spell gives you more than just the tail. You gain climb, darkvision, Low-light vision, swim and undersize weapon. Simply take the spell when you gain access to 4th level spells.
The other bloodline powers and spells from the salamander bloodline don’t really seem to fit with the lamia matriarch theme. Since are shapechangers the shapechanger bloodline might be more appropriate. Its 3rd level bloodline power will allow you to remain in lamia form longer. By the time you get the spell Monstrous Physique you can have it last 1 hour per level
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Synthesist Summoner with an Eidolon with the serpentine base form and the limbs(arms) evolution is another potential option.