Because I just can't stop thinking about LD, here are some ideas for each potential theme.

Unstable - A crazy scientist creates an unstable weapon, which you need to destroy. OR... You are the crazy scientist and you must craft this weapon/bomb. (Action crafting game)

Making connections - You are a sad teenager without friends, 24/7 on his/her computer. You must find someone you can be friends with (Story, text based, chatting similator)

One tool, many uses - Basically any kind of Terraria-like game

Decay - A monster slowly decaying. You must KEEP IT ALIVE (get it?!)

On / Off - There is a huge button that needs to be protected from hordes of people who want to push it ON or OFF. (Tower defence probably)

Delay the inevitable - You are dying, but before you die you want to leave something for your kids. You grow a farm, or build a house. And keep yourself as healthy as possible to finish the job (Story driven farming/building simulator)

Keep your distance - You are sailing across dangerous waters full of sea monsters. You must get to the other side without getting too close to any of the abominations. (Arcade, roguelike)

Delivery - You work as a post man in a sci-fi universe and you must deliver mail to your customers as fast as possible (Arcade, platformer, roguelike)

The environment changes you - You are a secret comando agent, going through a different biomes to complete each mission. You must prepate yourself for each of these biomes so you are advantageous before your enemies (action, arcade)

Leave something behind - Actually same or similar to "delay the inevitable"

Everything changes at night - When sun goes down, you are alone in your old house. You start to hear strange noises and feel uneasy. You must deal with these dark places. (Horror/Survival)

3 rules - Literally anything

Replication - You are a monster eating humans. Each time you eat a human you replicate. Now you have two monsters, then you will have four monsters... and so on. (RTS, Action arcade)

Strength in numbers - You grow some small community/colony and each level you must defeat more and more enemies (strategy - turn based or RTS)

Summoning - You are a small squirrel mad at the world for making fun of your size. So you decide you want to rule the world. But you can't do it yourself... You have to summon the demon to help you with that. (Story driven action platformer)

It follows you - You have a new puppy and it follows you everywhere. Your job is to train it well (Dog simulator, tamagotchi like simulation)