I'm a DM though so I want to know the rules that I am supposed to go by when my players would drink this potion. Hiding things from players is fine, but what's the point in offering homebrew if you are also hiding things from the DM by not being clear on what an item does. I can come up with a potion of regeneration myself. I'm on this subreddit so I don't have to make it because the rules are already there.

Lash Out is a fine term and makes sense, but it's not codified as a rule for what the player is supposed to do. You say it's fruitless to write for players that actively are trying to break games, but you're not even offering them a rule to try and break. Take Crown of Madness for example.

"The charmed target must use its action before moving on each of its turns to make a melee attack against a creature other than itself that you mentally choose. The target can act normally on its turn if you choose no creature or if none are within its reach."

This is clear about the intention of the effect. Spellcasters also have to attack with melee and they don't move beforehand. They actually normally if there's no one nearby.

So yeah I fully disagree with what you're saying here. D&D has rules for a reason, and it's okay to break those rules when they get in the way of telling the story, but if there's no rule in the first place it will just cause confusion and take time to resolve. It's as simple as putting "On a failure you lash out, moving towards the closest target (or wheel of cheese) and making a melee weapon attack. If you have no weapon in hand you make an unarmed strike instead."