Lack of time to start standby pump after duty pump failed

As per P&ID there are two pumps that were designed for duty and standby.

The auxiliary system was provided lubrication system with air cooler for each particular pump.

 There are lubricating pump motors, pressure switch, pressure transmitter and air cooler motor equipped in skid, the control and sequencing function by ICSS.
As per function is the auxiliary system running while main running (if main does not run then auxiliary system does not run as well).
As per function idea whenever the duty pump was failed but standby pump will not able started immediately because the sequencing function will go to start the lubrication pump, opening the solenoid valve and starting the air cooling fan and eventually start the main pump.
So there is some delay time between duty pump failed and standby pump run.