If my simplistic understanding is correct, there is probably a difference between Lag Phase and Lag Time. It seems like a lot of home brewers use them as synonymous. If we are determining Lag Time to be the time from pitching until we see krausen or airlock activity, it's almost certain that at that point our yeast are actually well into Log Phase.
I pitch active starters, from smack pack to oxygenated no-stir starter to beer in 8-10 hrs usually. My pitch test is simple. I gently osilate the flask and look for foaming. If there's activity, it's ready. I almost always have visibly identifiable activity in the beer within 24 hrs. Sometimes 12hrs or less, sometimes up to 48hrs, depending on the yeast and gravity and temperature. The colder you ferment, the more CO2 it can retain, meaning the longer it takes before it's visible.
Frequently someone posts a question similar to : I pitched X Lager yeast starter to my 1.050 wort at 70F ambient. I checked it 48hrs later and there's no activity. Is my yeast dead? After several answers and suggestions, they check gravity and find that it's done fermenting at about day 3... Magic! They actually missed fermentation, it went so fast.
Visible activity, especially airlocks, are not very reliable at telling us what is actually going on. Check gravity before freaking out, if it's only been a few days.