Hi,
Yes, the LPC5536/LPC55S36 has both internal DC/DC converter and LDO for VDD_CORE power supply, if you use internal LDO, it is okay to just connect a 4.7uF cap to the VDD_CORE pin.
You can connect 3.3V power supply to the VDD_MIAN and VDD_MAIN_PWR pins.
The remark "The internal LDO allows the MCU to use an external regulation element" just means that the 3.3V power supply which is connected to VDD_MIAN and VDD_MAIN_PWR can be from external DC/DC converter or external LDO.
For example, you have 5V power supply, there is an external Buck DC/DC converter which convert 5V to 3.3V, the 3.3V can power the VDD_MIAN and VDD_MAIN_PWR pins.
Hope it is helpful
BR
XiangJun Rong