LeeG, you are awesome! Thank you for taking the time to explain the details of the Log files and the Group commands.
I tried hooking up a different lamp, but I still had the same issue. However, after re-reading the LampLinc manual, I found the instructions for disabling this Load Sensing "feature" (which is enabled by default) After turning Load Sensing off, my lights now turn on at 30% instead of full power and my logs no longer contain the extra Group commands.
In case anyone else has the same issue, you can disable Load Sensing by performing the following on the LampLinc device:
1. Press & hold the Set button on LampLinc until it beeps (3 seconds)
The LampLinc Status LED will begin blinking green
2. Double-tap the Set button on LampLinc
LampLinc will beep and its Status LED will stop blinking and turn on solid green if the load is on or solid red if it is off
Source: http://wiki.smarthome.com/index.php?title=2457D2_Manual#Enabling_.2F_Disabling_Load_Sensing_on_LampLinc
Thanks again LeeG and Michel for your quick responses and vast knowledge!