I'm a little more than half-way through my Tea Sommelier training, and am a professional coffee buyer/taster. I'd be happy to help if I can.
Lapsang Souchong tea is a fully oxidized (making it a "black" tea), Chinese, tea prepared by drying the finished leaves over fires (typically of pine) which creates its characteristic smokey flavour. It is generally considered the smokiest of the smoky teas. Keemun (also a Chinese fully oxidized tea) can also present smoky character, look for Keemun Mao Feng for this characteristic.
With my Virginia tobaccos, I like to drink a white tea, they undergo very little oxidation and are prepared from only the young bud of the tea bush. Flavours of white teas are floral, ranging into peachy sweet character. They are delicate teas, and are very complimentary to a less intense pipe.
With a heavy tobacco, something that is Latakia forward, or spicy and Oriental, I also like to go with a Lapsang Souchong. But I would also recommend a fresh, bright and sweet Darjeeling, or a deep heavy and full Assam.
If you're looking for green teas, you can't go wrong with the fresh, cut-grass, and approaching bitter green of a Japanese tea like Gyukuru. If you want something more robust, pick up Genmaicha which has puffed (almost burnt) rice included in the tea for a roasted nut character.
Have fun with your teas, like you do your tobaccos, and I guarantee a doubling of your puffing and quaffing experience.
Cheers,
-- Pat