Q: can I use a password for my ID Apple with all lowercase letters?

Your security ...

Apple ID: Tips for protecting the security of your account

This is the Apple screed.

When changing your password, your new Apple ID password should:

• Be at least eight characters.
• Contain at least one number (0-9).
• Contain at least one uppercase letter (A-Z).
• Contain at least one lowercase letter (a-z).
• Not contain three consecutive identical characters.
• Not have been used in the past year.
• Not be the same as your Apple ID username.

On this basis the answer would be NO

But ... it uses the word SHOULD, not MUST.  And that could be interpretted to mean it is flexible.

The Apple Support Communities are an international user to user technical support forum. As a man from Mexico, Spanish is my native tongue. I do not speak English very well, however, I do write in English with the aid of the Mac OS X spelling and grammar checks. I also live in a culture perhaps very very different from your own. When offering advice in the ASC, my comments are not meant to be anything more than helpful and certainly not to be taken as insults.

In this case should is the not flexible version.

No, you cannot have an all lowercase Apple ID password.

Why are you being so dufficult about this? Apple has changed the password requirements to increase the security of the system. What was the past no longer applies.

Surely you don't want your account to get hacked.

That's why I posted the link in my first reply to you...   give it a read.