Are your server experiencing similar high load during the backup time, there are two spikes in your graph at night time.
You need to check your server when the I/O wait is high, pay attention to "SWAP" memory being used, if for some reason the server start to use swap, you need to find out which process causes it.
And you can reduce "Max conn" for lsphp to avoid starting too many lsphp processes. when your server is short of memory, running more lsphp will only make it worse.
Another suggestion is to run Apache for a day or two and compare the load graph with that of LSWS.