Potrzebuję toalety

Now you are probably looking at 'toalety' and thinking - it ends in 'y' so is this actually an 'a' ending word in the Genetive case - after a verb when something is missing or lacking.

Well you are absolutely right - it is Genetive.

When we need something it is because we don't have it - that means it is missing / we are lacking it.

This means 'potrzebuję' puts us in the 'Genetive' case.

Understanding cases and then remembering the endings is the hardest part of the Polish language but if you get in the habit of thinking through 3 steps:

1. Am I talking about what/where something is? - Use Nominative - 'Gdzie jest toaleta'
2. Am I using a verb positively? Use Accusative - 'Mam toaletę'
3. Is something lacking or missing? Use Genetive - 'Potrzebuję toalety'

The more you practice these 3 steps the faster your thinking process will become until it is something you do without needing to try.

Just like in English 'Potrzebuję toalety' means you need to go(!). Something you would say to a friend.

When talking to a stranger you would say 'Szukam toalety' or 'Gdzie jest toaleta?'.