Can I pitch an idea to LEGO?
LEGO doesn't directly take product ideas from fans.  

However, there is a website called LEGO Ideas where you can post creations that may potentially get turned into official LEGO kits.

The process is as follows:


Submit your idea to LEGO Ideas.  Take some time to get good pictures, and write a good description, or your idea will probably not make it off the ground.
Get votes for your idea.  The way LEGO Ideas works is that ideas that can get 10,000 supporters (votes) in a year will get put into a review process.  The best way to get votes is to share your idea.  Tell your friends, and spread it on Facebook or other social media.
Go through the review process.  Once you reach 10,000 supporters, your idea goes to the LEGO review board.  The review board will look at your idea, and decide if it is worth creating as an official set.  Things like size, cost, part complexity, new parts, and licensing will all be factored in to the review.  Be away that only about 1 in 10 ideas that reach the review board are approved by the review board.
Buy your new LEGO product.  Once the review board green-lights your idea, it will be turned into an official LEGO product!  The products are often, but not always, limited edition kits, so get them while they last - as the creator you are given complimentary 5 sets and 1% of net sales.


Hopefully, this will give you some background on the LEGO Ideas process if you want to pursue that route to get your idea turned into an official LEGO kit.