Installing a bootloader on an ARM Microcontroller
Both devices have on-chip bootloaders that will always be executed. With the LPC17xx, you can write a secondary bootloader to execute custom code that will run directly after. You simply need to direct your IDE to place the code at location 0x00.

On the documentation page, have a look at AN11257 and AN11258. These discuss creating secondary bootloaders (SBL) to load code from SPI or I2C respectively. This could retrieve code from a PC or an external memory device.

From AN11257:


  In these MCUs, the primary  boot loader resides in the boot block. The
  boot loader is executed every time the part is  powered on or reset.
  It can execute the ISP command handler or the user application  code,
  which is stored in sector 0 of internal flash memory.
  
  The SBL in
  this project refers to a user-defined application that provides the
  user with an  option to update the User Application Firmware or
  execute the previously programmed  User Application Firmware. It is
  placed from the address 0x00 so that when the primary  boot loader
  runs user application, it executes first.


I couldn't find similar documentation on the LPC13xx. But it's primary bootloader has a bit more functionality built-in. Specifically the ability to load new programs via UART. Your version lacks the USB functionality they talk about in the User Guide:


  The bootloader code is executed every time the part is powered on or
  reset (see  Figure 63). The loader can either execute the ISP command
  handler or the user  application code, or it can obtain the boot image
  as an attached MSC device through  USB. A LOW level during reset at
  the PIO0_1 pin is considered an external hardware  request to start
  the ISP command handler or the USB device enumeration without 
  checking for a valid user code first. The state of PIO0_3 determines
  whether the UART or  USB interface will be used:
  
  • If PIO0_3 is sampled HIGH, the bootloader connects the LPC134x as a
  MSC USB  device to a PC host. The LPC134x flash memory space is
  represented as a drive in  the host’s Windows operating system.
  
  • If PIO0_3 is sampled LOW, the bootloader configures the UART serial
  port and calls  the ISP command handler.
  
  Remark: On the LPC131x parts (no USB), the state of pin PIO0_3 does
  not matter.


You can still make the first instructions executed after the primary bootloader act as a custom secondary bootloader. You just need to locate that code at the proper address. How this is done is heavily dependent on your IDE. Refer to your IDE's documentation on how to properly control code placement into the desired sectors.