My understanding of it yeast cells will replicate in when their individual cell mass increases, ie they get fat and healthy they split. So what makes them fat and healthy, three things O2, nutrients and sugar, so when ever these are present they will get fatter and replicate.
The "lag" time is when we don't see any activity in the starter or wort and so we think nothing is happening there is stuff happening and it is just less noticeable as the number of cells doing it is so small. The reason that this is when all the reproduction is happening is there is an abundance of sugar, O2 and nutrients in the fresh wort, the longer the yeast has been in there the less of everything there is in the wort.
The phases are timelines and words we use to describe the yeast activity we observe I don't think that the yeast only do one thing in one stage. There really is only two things the yeasties do, aerobic and anaerobic fermentation, anaerobic makes alcohol and is more stressful to the yeast hence they get weaker and eventually die if pushed hard (high ABV) enough, while aerobic is what they like to do and it makes them fat healthy and then they replicate.
Now this part really is a guess or a point for discussion but I think that yeast would start replicating again if given more O2 and nutrients even if anaerobic fermentation had begun. An example of this, stir plates provide a higher level of continuous gas exchange and hence more cell growth. Does this mean that there should be a longer lag phase as there is more reproduction, no of course not.
Let the last setup of my starter ferment out, I use my stir plate for about 18-24 hrs and I then leave the yeast to sit for another 24hrs before cold crashing, when the yeast are running out of sugar in the wort they will start getting ready to hibernate, this process is then accelerated by the cold crash you give them a few hrs later. Come brew day, I decant make a starter (not on the stir plate) for yeast the morning of the brew to wake them up and get them going. I then pitch this whole starter hence why I don't use the stir plate for this one as I don't want oxidized wort going into the main wort. I'm not looking for cell reproduction only happy awake yeast ready to go to work.
Clem