Lake Peak does involve some scrambling, but I wouldn’t call it a lot. The summit itself is rocky and does require some easy scrambling. Lake Peak is a lot easier than, say, Marion Mountain in the San Jacintos (if you’re familiar with that peak). The majority of the peak is actually pretty flat.
You do have to have some comfort with cross country navigation. You can go up out of either Fish Creek or Lodgepole Saddle. Lodgepole Saddle is the small saddle on the east side of Zahniser Peak between Mineshaft Saddle and Fish Creek Saddle.