Hello. I like your deck. +1 from me. I have a suggestion. -4 island +4 Cavern of Souls would be a nice fit in this deck.

Tidebinder Mage and Thassa

absolutely beautiful i love merfolk and have always wanted to make one looking here id say you have the most simplistic and decent deck build i'v seen. the only thing id change is dropping in some Mana Leak . they can replace your one drop merfolk Cursecatcher . it could counter more creatures and quick spells sooner and with more of a safety in mana cost. personally i'd also take out Door of Destinies as there are a lot of quick paced decks out there that could slow you down if they kill-spell every creature you drop. in place id put in another simple one drop merfolk or perhaps if i were you id look into finding some zendikar merfolk. rise of eldrazi set also has some pretty strong merfolk that level up. one good choice could possibly be Coralhelm Commander with that being said i REALLY wanna play you with my mono-black budget deck. and you definitely get a +1 from me :)

I'd go -4 on the Tideshaper Mystic and go for a playset of Spreading Seas . The latter gives all your guys islandwalk and filters through your deck a little by letting you draw a card, and it's not like you'd be attacking with the Mystic in the first place (you've gotta make islands somehow, am I right?)

Lord of Atlantis is not allowed in Modern, Only cards printed from 8th edition and beyond. It's easy to tell simply by the background change that happened when it was printed. Coralhelm Commander is the perfect replacement and its cheap. I agree that this deck needs Cavern of Souls however, they come with a big price tag. It's worth it though if you can afford it because blue is probably your worst enemy. As for inexpensive upgrades, Kira, Great Glass-Spinner and Tidebinder Mage are staples for the sideboard. Also if you can find room for a set of Mana Leak that would be beneficial, at least in the sideboard if nothing else.

Metamorphic1992 Lord of Atlantis was reprinted in Time Spiral, so it is legal.

As for the deck, I would add some Phantasmal Image so that you can essentially have 12 copies of your 2 drop lords.

its never shown up in my modern searches but you're correct. I also didn't know that time spiral timeshifted is legal in modern despite having an old style background.