I can't give you the Lakes data but you can check what the high/low/average temperatures are for the summit for the past four years for those dates by looking at our WS Form F-6 (http://www.mountwashington.org/weather/f6/). Just click on Sept for each year and then it looks like an excel spreadsheet of dates on the left and column descriptions across the top. Just figure Lakes will be a few degrees wamer or cooler at times. Sept is the month we usually get our first inch of snow on the peak and we have already hit freezing a few times this month. So it's that time of year again folks that you have to pack in layers because it might be summer-esque one day and full on fall the next.
Staff Meteorologist/Night Observer, KMWN (Mt Washington Obs., NH)