Does it look unprofessional for a client to give their psychologist a birthday card or Christmas card with money or a lotto ticket?

Don't give money. The lotto ticket is okay. 

It's a nice thought. Just give them some

Christmas cookies. 

I'm not sure why people are saying it's unprofessional.

You are the patient. You are not expected to be "professional."

Only the doctor is. 

I just think giving money is a little too personal. 

It doesn't LOOK unprofessional, it IS unprofessional as well as being inappropriate. 

I doubt you would ever know it was their birthday.

Professional implies that there is a working or business relationship between the persons. Money or a lotto ticket in a professional setting is unprofessional.

In terms of a client giving money or a lotto ticket to a paid professional with whom they have no professional or personal relationship, it is unprofessional or even bribery.

To enclose money or Lotto tickets is tacky, but a card is fine.

Just give the card, don’t put anything else in it