If you can get the wood you need for blanks locally as boards and then process them yourself, that's definitely the best way to go! The problem is, many of us love to work in exotic woods that are not native the the areas we live in, like ebony, cocobolo, olivewood, ect ... for those we order them online, for the most part, or get very lucky to have a nearby cabinetry shop that has offcuts and discards that we could use!
Kiln and air-dried lumber has a moisture content of around 8% - 12%, which is quite sufficient to be used on your lathe. At those moisture levels, they probably will NOT decrease any further, and thus your project should turn out to be quite stable. Turning woods over 20% moisture down to final measurements should be avoided, as the wood will continue to shrink further as it tries to reach equilibrium with the environmental moisture content around it .... the same goes for wood that has been dried down to under 8% moisture, as that will likely attempt to absorb moisture and "grow" after you've turned it.
The process of sealing and finishing your project when completed should prevent the moisture content of your item from changing, and thus protects the wood and finish from cracks and splits as time passes by, but you should be aware that freezing temperatures can still cause damage, especially with higher moisture content items.
"Green wood", that is to say, freshly cut lumber that hasn't been kiln dried or air dried or been left on the ground where it fell for longer than one year to reach equilibrium, can be turned on a lathe as well. Typically, it cuts easier and much more readily than aged or dried wood, but it finishes poorly, as the wood is much more saturated with water and oils. With modern lathes, green wood is generally only turned to "rough measure" and then dried or aged till it is low enough in moisture content to finish the turning down to final measurements. An additional method that I have heard of is to boil the rough turned blank in water to drive out all the remaining oils and sap, leaving just water soaking the blank, which can then easily be removed by letting it sit on a shelf to air dry or dry it in a kiln. I have also heard of microwaving smaller pieces to drive out the oils and water, but I've never tried any of these methods.
In short ... if you can get your wood in bulk as board feet of lumber, then by all means DO IT! But if you're looking for something exotic, well, that's a special order kinda thing ... Last I checked at the local lumberyard, I can order Ebony for my projects .... but the minimum order for it would be 100 board feet at 90 dollars per board feet...
I'll take a 4-pack of pen blanks for 12 bucks, please! I worked out the cost of Bethlehem Olivewood in board feet as well, just because I wanted to know ... it's around 128 dollars a foot!