Would the lysogenic cycle for the reproduction of viruses be considered a form of naturally occurring transformation since DNA from the virus is being incorporated into the DNA of the host cell?
The answer lies in the definition itself of transformation. See from here:
In molecular biology, transformation is the genetic alteration of a cell resulting from the direct uptake and incorporation of exogenous genetic material from its surroundings through the cell membrane(s). For transformation to take place, the recipient bacteria must be in a state of competence, which might occur in nature as a time-limited response to environmental conditions such as starvation and cell density, and may also be induced in a laboratory.
What is clear from this definition is that host cell needs to be competent for taking up extracellular DNA to call the process transformation. Also, the term
direct uptake does not seem to fit here as, you know why, bacteria do not just go on collecting viral DNA from their surroundings.
Obviously, bacteria are not competent to take up viral DNA, nor the virus makes them so. The virus simply injects and joins its own DNA into baterial genome. Now, it would be some common sense to know that the host does not like it, so whether it is competent or not, is just a matter of debate (did anyone ask them?). In short, No, the process of lysogenic cycle would not be considered transformation as the bacteria are not made competent for this process.