None of the above. Alcohol increases the cancer risks when taken in conjunction with tobacco smoke. Try a good strong tea hot or cold. Plenty of of varieties to match what you're smoking. I've found Jasmine complements Lakeland flavors well and Oolong goes well with English blends.
That said, if you don't mind the increased risk, Basil Hayden and LBF are a fine combination.
Really, there is no ONE best answer. As with any flavor pairings its all about finding the match/mix you like
I was going to say Tea is great with all tobacco. Water is outstanding.
Cabernet, Merlot, and Malbec go well with Latakia blends. Also whisky, scorch and bourbon.
Burley and Virginia Go well with any beer, ale, stout etc.
Virginias, Burley and Perique blends go well with Absinthe. Benefiting the Absinthe more than the pipe tobacco.
Randelli, have a good Lapsang Souching recommendation? I've not explored that style much. Its nice to see I'm not the only tea drinker here.
Also, barley tea and Burley, beyond being alliterative, go well together. I've been smoking the 401 Burley from Milan recently with my barley drink.
I like Harney and Sons tea. I order from there. I haven't had the Lapsang, that's the smoky stuff, isn't it? Assam is great with a pipe. Keemun also. Ceylon UVA Highland goes great with Old Dark Fired. Tea it's what's to drink when you smoke. Idealy.
Coffee, tea, and fruit juices are my goto drinks with any tobacco. Sweet iced tea, Southern style of course. But, Mountain Dew and a good straight Virginia is nice also. The acidity compliment as each other IMO. But, in a pinch iced water is good as well. I always have a cup of something with my smokes, always.
If I am into the tobacco blend and the pipe themselves, the best is tea, and my favorite black tea is P&G Tips. Water is second, best if crisp and cold. Bourbon and water and occasionally a single malt Scotch can be a heightened experience but can shoulder over the leaf. Other beverages work -- beer, wine, coffee, hot chocolate -- but coat the mouth and mask a good blend, for me. Colas not so good, the whole sugar or sugar sub thing just doesn't go.
I grew up with Twinnings so it is always a brand I'll reach for. Other than that, I go to my local Asian supermarket and pick up stuff that looks interesting. And I buy frou frou "chai" tea blends from Teavanna for my wife.