Yes. Zoomblr shows live's public posts and profile picture with no Tumblr account or login required. It's completely free.

Open live on Zoomblr and tap the download button on the avatar to save the full 512px image in its original format (JPG, PNG, GIF, or WebP).

Each image in live's feed has its own download button — tap it to save the picture in full resolution. Photosets give you a button per image.