Saturated Transimpedance Amplifier Issue
You're overloading the amplifier. Recovery from overload can be very fast, but 1 millisecond is not uncommon, and tens of ms is possible even with multi-MHz GBW op-amps. 

There are amplifiers such as the OPA380, which has 100ns overload recovery. 

I don't see a number for the LF357, you can measure it, as suggested in this classic application note AN356 from Analog Devices.