If you are looking for a strictly SimpleDB solution (as per the question as stated) Katta and Lucene won't help you. If you are looking for merely an 'Amazon infrastructure' based solution then any of the choices will work.
All three options differ in terms of how much setup and management you'll have to do and deciding which is best depends on your actual requirements.
SimpleDB with a multi-valued attribute named Keyword is your best choice if you need simplicity and minimum administration. And if you don't need to sort by relevance. There is nothing to set up or administer and you'll only be charged for your actual cpu & bandwidth.
Lucene is a great choice if you need more than keyword searching but you'll have manage updates to the index yourself. You'll also have to manage the load balancing, backups and fail over that you would have gotten with SimpleDB. If you don't care about fail over and can tolerate down time while you do a restore in the event of EC2 crash then that's one less thing to worry about and one less reason to prefer SimpleDB.
With Katta on EC2 you'd be managing everything yourself. You'd have the most flexibility and the most work to do.