The very specific code you are posted seems not active. Which might not be a problem, LPCOPEN is AFAIK a predecessor of the current MCUXpresso SDK, and supported for backward compatibility reasons. This might not be used/enabled in your application.
I would suggest to search for CMSIS in your startup code. For me, it looks like this (in startup_lpc54628.c):
#if !defined (__USE_CMSIS)
// Assume that if __USE_CMSIS defined, then CMSIS SystemInit code
// will enable the FPU
#if defined (__VFP_FP__) && !defined (__SOFTFP__)
//
// Code to enable the Cortex-M4 FPU only included
// if appropriate build options have been selected.
// Code taken from Section 7.1, Cortex-M4 TRM (DDI0439C)
//
// Read CPACR (located at address 0xE000ED88)
// Set bits 20-23 to enable CP10 and CP11 coprocessors
// Write back the modified value to the CPACR
asm volatile ("LDR.W R0, =0xE000ED88\n\t"
"LDR R1, [R0]\n\t"
"ORR R1, R1, #(0xF << 20)\n\t"
"STR R1, [R0]");
#endif // (__VFP_FP__) && !(__SOFTFP__)
#endif // (__USE_CMSIS)
To be sure, you can fire up the debugger, and check the FPU init code is executed. Or check the respective flags in the core config registers afterwards.
For LPCopen / LPCware, I am no expert, though.