There are several reasons for lag time in your beer:
If you are ever concerned about it dust off your hydrometer and compare a reading to the estimated original gravity, if it is fermenting or has finished fermenting then the hydrometer will cue you in to where things are at.
Remember that wort is most vulnerable prior to fermentation so take a sample with utmost sanitary concern. Also trust your senses, if it has fermented it will smell like beer and there will be a foam ring indicating a krausen.
Ferment times can easily vary from 24 hours to 10 days depending on the conditions and yeast strain employed. Activity will vary from batch to batch since there are so many variables affecting performance.
Damaged yeast from shipping or improper storage conditions at home, may take time to propagate and “heal” and lag times up to 3 days are not uncommon.
Any doubt about the viability of the yeast, make a yeast starter, to give the healthy cells an opportunity to propagate. E.G.: extreme hot or cold temperatures, expired yeast.