From the website:
http://www.LittleBigPlanet.com/en-us/game_guide/ps3/downloadable_content/metal_gear_solid_level_kit/
no not legally
There is both a Level Kit and a Costume Kit for Metal Gear Solid
There is a Metal Gear solid Level Kit and Costume kit both are $5.99
It is available and included with the Metal Gear Solid costume pack for $5.99 and as a Metal Gear Solid Snake costume for $1.99 from the Playstation Store
There is a Metal Gear Solid costume Kit and a Metal Gear Solid Level Kit at the Playstation Store for $5.99 each or the individuals costumes are $1.99
Neon materials for building come from the free metal gear solid pack and the neon skin material comes from finishing the bunker
By purchasing the metal gear solid game pack
Buy the metal gear solid add on content from playstation store and you'll get it in the levels
The GOTY comes with some free add-ons like Metal Gear Solid Pack, History costumes, and more. It also comes with a beta to Mod-Nation Racers. The normal LBP just comes with the game and the information packet.
Download the MGS4 pack from the Plystation Store. It is free, I believe.
You either need to have a friend that already has it or you need to buy the Metal Gear Solid pack which is $5.99
Metal Gear is the name of the bi-pedal tank the game's, Metal Gear Solid, main mission is based around, the Solidpart comes from Solid Snake: the main character.