Chris, I don’t pretend to know enough about how organisms manage their genomes to say, and I don’t think anyone else does either. The studies that Jim Shapiro referenced in his 2011 book in support of “natural genetic engineering,” however, were mainly about bacteria, so if it occurs it is not restricted to more “advanced” life. It is certainly true, however, that the reason all biological experiments lack the precision of experiments in physics is that organisms always react in more compex ways than do molecules.
On the other hand, since I read R J Russell in 2012 I’ve been keeping an eye on the literature for evidence that quantum events actually can bias mutations to alter the macro world. So far, the consensus appears to be that they cannot, and that quantum indeterminacy, whatever determines that, really does disappear into the larger scale processes of the macro world. The consensus may be wrong, but since it would radically change how quantum mechanics affects the world, it needs to be demonstrated rather than assumed.
If that is the case, then the mutations in Lenski’s bacteria would be due to bog-standard Maxwellian statistical randomness, that is, determined by the usual physical forces, and only random with respect to our ignorance. I’m unaware, outside of quantum events, of any evidence that natural laws vary to create physical indeterminsm. Are you?
That leaves the question of divine foreknowledge or agency exactly as it was before, only (as I’ve often reminded people) Maxwell himself was in no doubt, regarding statistical mechanics, that it did not lessen divine providence:
Would it not be more profound and feasible to determine the general constraints within which the deity must act than to track each event the divine will enacts?
Of course, if one wants to explain why a particular mutation happens, one would have to track the individual events, but it would leave as a matter of worldview choice whether the events were enacted by God, or by some as yet undiscovered force called “chance.”
But always remember that probability distributions are only and always measures of our ignorance (in the form of abstractions), and never causes of anything in the real world.