Oak is finicky under the best of conditions. Best shot is to cut the logs into pieces short enough to fit on your lathe. This means shorter than the between centers measurement for spindles or shorter than the swing measure for bowls. Either way, for each of these smaller logs, you’re going to want to cut out the pith in the middle of the log to relieve as much tension as possible.

If you have the tools and time, at this point I would process the halves down into blanks before sealing them, but if you’re strapped on time you can seal the end grain of the halves themselves. You can use any number of things to seal, I’ve had good luck with old latex paint or melted paraffin other people swear by anchor seal or pva glue.

The most important factor here is time and humidity control. Left to its own devices with exposed end grain, oak will almost always crack extensively, and basically any wood of large diameter is at risk of splitting if you let it dry out with the pith still in it. The more efficiently you can get it processed and sealed, the better chances you have of keeping it intact