I am always receiving e-mail messages from employment agencies promising that they would take me for a breakfast and at times for a lunch.

How differently am I supposed to prepare for the two?
What sort of clothing am I supposed to put on?

How is the lunch etiquette different from the normal interview of sitting in front of the panel in an interview room?

Inviting a client for a meal can be a way of having an informal chat, much less formal than an interview. It also allows the agency to form an opinion about your suitability for various types of jobs such as selling, where you may yourself be expected to entertain clients. They can assess whether you are comfortable in a social environment, able to manage a menu and wine list, and make small talk and potentially put clients at ease.

Prepare for both in the same way as you would for any interview, if you know the type of positions they are offering. If not, research the agency itself, read its website, and search the internet for reviews.

I have covered this topic in depth on the site, it will be worth your while to reread this whole section, which includes interview questions and answers
Prepare For An Interview

Beware of paying them any money to go on their books!! If this is what they are doing, then you will see that on the internet if you conduct an in-depth search for reviews and feedback

I suggest you wear business dress for both.

The etiquette of any interview is the same whether it is held in a restaurant or in an interview room with a panel. Listen carefully to the questions and give a full answer. Be polite at all times. Etiquette is simply good manners.