We have some LWAPP AP's that use power injectors with no issues. You may have to enter the following info in the WLC;
While the AP boots, with its Intelligent Power Management feature, it negotiates with the switch via Cisco Discovery Protocol messages in order to provide the necessary power to the AP. Even though the power injector is connected to the AP, the AP that uses this Intelligent Power Management feature gives priority to the Cisco Discovery Protocol information in order to identify whether or not the switch can provide the power. Therefore, after the Cisco Discovery Protocol message shows that the switch does not provide sufficient power (since it is not an inline power capable switch), the AP disables its radios. At this time, the status LED of the AP turns orange and this error message is recorded:
[ERROR] : AP has not enough in-line power
to enable radio slot 1 In order to overcome this problem, issue the
config ap power injector enable installed
command on the controller that is connected with this AP. This command is available from controller version 220.127.116.11. Ensure that you use the correct version in the controller.
This command specifies that a power injector is used in order to supply sufficient power to the AP.
From this doc;
Cisco Aironet and WLAN Controller Product Power Options