Wireless audio from P.A. System to DSLR
There are a lot of variables in this equation, and any one of them could be the culprit.  These include: the quality of the audio picked up by the lapel mic, the quality of the PA preamp, the quality of the PA signal output to the wireless transmitter, the quality of the wireless transmitter, the quality of the wireless receiver, and finally, the quality of the DSLR's audio preamps.

I would start eliminating variables by feeding a known test signal (such as an NPR podcast) into the DSLR audio port, and if that's good, feeding the same signal to the wireless transmitter/receiver pair into the DSLR.  If those, too, are good, then your PA system is the problem.  If, on the other hand, you cannot get decent audio into your DSLR from a known good source, you are not going to get decent audio into your DSLR from your PA.  Which is perhaps why so many DSLR shooters use external audio recording devices--not because they want to go crazy editing audio, but because they don't want to go crazy editing audio.

Regardless, the most reliable way to solve this problem is to introduce and eliminate variables one at a time.