Alright, these are extremely rough first drafts; I'm not happy with these at all, but hopefully they will at least provide a foundation to begin hashing out what a lung dragonborn should have. For example, some species have a Water Fire ability, almost all species can breathe water, and many species can fly. Coiled Dragons are good at crushing things, Typhoon Dragons have an affinity for wind, thunder and lightning, Spirit Dragons are the diplomats of the species... there's potential here, I just wish I knew how to unlock it!
Carp Dragonborn (Yu Lung)
Ability Score Modifiers: +2 Wisdom, +1 to one other ability score of your choice
Size: Small
Speed: 25 feet, Swim 30 feet
Vision: Normal
Amphibious: You can breathe water and have a Swim speed of 30 feet.
Blooming Wisdom: When you need to make a Wisdom check for a skill you do not have Proficiency in, you may still apply half of your Proficiency bonus (rounding down).
River Dragonborn (Chiang Lung)
Ability Score Modifiers: +2 Wisdom, +1 Charisma
Size: Medium
Speed: 30 feet, Swim 30 feet
Vision: Normal
Amphibious: You can breathe water and have a Swim speed of 30 feet.
Cloud Step: You do not take damage from falls if you are not Restrained, and you are always considered to have a running start when making Jump checks.
Cause Rain: As an action, you can exhale storm clouds, causing the weather to change to gentle rain within a radius of miles equal to your Charisma score. The rain lasts for a number of hours equal to your Charisma modifier, and once you have used this ability, you must complete a long rest before using it again.
Earth Dragonborn (Li Lung)
Ability Score Modifiers: +2 Wisdom, +1 Strength
Size: Medium
Speed: 30 feet, Fly 20 feet, Burrow 20 feet
Vision: Darkvision 60 feet
Wings: You have a pair of wings which allow you to Fly at a speed of 20 feet. You cannot fly if you are wearing medium or heavy armor, or if you are encumbered.
Stone-Shaper: You can cast the Mold Earth cantrip (Xanathar's Guide) and have a Burrow speed of 20 feet.
Sea Dragonborn (Lung Wang)
Ability Score Modifiers: +2 Wisdom, +1 Constitution
Size: Medium
Speed: 30 feet, Swim 30 feet
Vision: Normal
Amphibious: You can breathe water and have a Swim speed of 30 feet.
Armored Scales: When not wearing armor, your AC is 13 + your Constitution modifier. You can use your natural armor to determine your AC if the armor you wear would leave you with a lower AC. A shield's benefits apply as normal while you use your natural armor.
Breath Weapon: As per standard dragonborn damage, a cone of Steam - this inflicts Fire damage, but can function underwater.
Coiled Dragonborn (Pan Lung)
Ability Score Modifiers: +2 Wisdom, +1 Intelligence
Size: Medium
Speed: 30 feet, Swim 30 feet
Vision: Normal
Natural Weapons. Your fanged maw and constricting
serpentine body are natural weapons, which you
can use to make unarmed strikes. If you hit with your
bite, you deal piercing damage equal to 1d4 + your
Strength modifier. If you hit with your constrict attack, you deal bludgeoning damage equal to 1d6 + your Strength modifier, and the target is grappled (escape DC 8 + your proficiency bonus + your Strength modifier). Until this grapple ends, the target is restrained, and you can’t constrict another target.
Amphibious: You can breathe water and have a Swim speed of 30 feet.
Cloud Step: You do not take damage from falls if you are not Restrained, and you are always considered to have a running start when making Jump checks.
Spirit Dragonborn (Shen Lung)
Ability Score Modifiers: +2 Wisdom, +1 Charisma
Size: Medium
Speed: 30 feet, Swim 30 feet
Vision: Normal
Amphibious: You can breathe water and have a Swim speed of 30 feet.
Cloud Step: You do not take damage from falls if you are not Restrained, and you are always considered to have a running start when making Jump checks.
Tail Slap: You can make a tail slap as an unarmed strike. If it hits, you deal 1d8 + Str modifier Bludgeoning damage.
Celestial Dragonborn (T'ien Lung)
Ability Score Modifiers: +2 Wisdom, +1 Charisma
Size: Medium
Speed: 30 feet, Swim 30 feet
Vision: Normal
Amphibious: You can breathe water and have a Swim speed of 30 feet.
Cloud Step: You do not take damage from falls if you are not Restrained, and you are always considered to have a running start when making Jump checks.
Breath Weapon: As Dragonborn, Cone of Fire, Dex Save.
Typhoon Dragonborn (Tun Mi Lung)
Ability Score Modifiers: +2 Strength, +1 Charisma
Size: Medium
Speed: 30 feet, Swim 30 feet
Vision: Normal
Amphibious: You can breathe water and have a Swim speed of 30 feet.
Cloud Step: You do not take damage from falls if you are not Restrained, and you are always considered to have a running start when making Jump checks.
Thunderborn: You have Resistance to Thunder & Lightning Damage.
Stormbringer: You can cast the Gust, Shocking Touch and Thunderclap cantrips, all using Charisma as your spellcasting ability score.