Problem Statement
When using the Raspberry Pi 3 Model B with the LoveRPi 5V 2.5A MicroUSB Power Adapter Revision C, some users experience the rainbow square or lightning symbol on the top right of their screens.
Cause

The Raspberry Pi 3 Model B schematic shows the design of the power input. The power pin of the MicroUSB port is linked to a polyfuse and a diode before becoming the 5V rail (GPIO Pin 2 and 4). It has an APX803 supervisor chip on the 5V rail that detects if the voltage on the rail drops below 4.63V. The supervisor chip sends a signal to the SoC via PWR_LOW_N wire which is read by firmware. When you measure power from the GPIO header, you are measuring the 5V rail and not the MicroUSB input voltage.
The LoveRPi 5V 2.5A MicroUSB Power Adapter Revision C is designed to be a standards complaint, true 2.5A high current, low noise, flat V/A slope, UL certifiable power adapter built specifically for single board computers. It is designed to have a mean voltage deviation of less than 2% for 20-80% load range while fitting in the 5% range recommended by the USB specification.
0.0A: 5.15Vmax
0.5A: 5.10V +- 0.075V
1.0A: 5.05V +- 0.075V
1.5A: 5.00V +- 0.075V
2.0A: 4.95V +- 0.075V
2.5A: 4.90V +- 0.075V
The Raspberry Pi 3 Model B power input design will experience a voltage drop of up to 0.3V between the MicroUSB input and the 5V rail at high current. Even if the MicroUSB input has the proper voltage, the voltage on the 5V rail could be as low as 4.6V. The power input circuit design is outside of the bounds of what we can control. This design forces businesses to create and customers to purchase power supplies that are out of compliance with industry standards.
The reason some other power adapters do not experience this issue is because they provide dangerously high voltages that are not standards complaint. In our tests of this issue, we found power supplies delivering up to 5.7Vopen and 5.5V with an 0.5A load. These may fry sensitive USB electronics that do not have any protection built-in.
Below is some of our oscilloscope captures to help explain the issue. The yellow line and readings are for the voltages at the input at the MicroUSB pins. The light blue line and readings are for the voltages at the 5V rail on the Raspberry Pi 3 Model B as measured through the GPIO header.
0.5A Low Current Reading (MicroUSB Pin vs GPIO Pin)

2.0A High Current Reading (MicroUSB Pin vs GPIO Pin)

If you have an oscilloscope, you can also verify this data.
Resolution
It is our opinion that the Raspberry Pi Foundation should change their design as this setup also causes issues with their own Raspberry Pi 7" Display. Instead of the APX803-46SAG supervisor chip, they should use the APX803-44SAG supervisor chip.
Our power supply will not cause any shutdown, crashes, throttling, or errors other than the cosmetic icon so the warning that you see is not consequential. You can turn off the warnings if they bother you by adding the following line to /boot/config.txt:
avoid_warnings=2