When you're writing a 1, you are writing 0x01, which will set only the lowest bit. You'd need to write 0x03 (you may write GPIO_PIN_0 | GPIO_PIN_1 instead if that's more clear) to set both LEDs:
GPIOPinWrite(GPIO_PORTB_BASE, GPIO_PIN_0 | GPIO_PIN_1, GPIO_PIN_0 | GPIO_PIN_1);
Look up the GPIOPinWrite function in the peripheral driver lib manual for more info.
It looks like you're already using the peripheral driver library (driverlib), so I'd suggest using it to enable all the modules (SysCtlPeripheralEnable), and for most operations in general. It'll make it easier to read, and easier to port between MCUs. The port #defines should be done for you already (somewhere....), I've never had to manually #define the memory addresses.
Also, you should check if the port is ready for use in a while loop. Currently, you check if it's not ready, and if not just give up. Use a while loop to continually check the ready status until it is ready. You should move that check a few lines up, to before you write to their configuration register.
Finally, I'm confused about which MCU you're using. I can't find any TM4C1230H6PM launchpads. Are you using a TM4C123GH6PM?
The reference manual for the MCU says that using RCGC2 is only for legacy applications. They suggest using RCGCGPIO instead, though I'd suggest using the driver library more fully, so you shouldn't need to worry about that, anyway.