A processor capable of running Linux is very different to an LPC8xx MCU. Apart from other things, below, typically a system running Linux will be physically larger than an MCU-based system.
It is highly unlikely that you will find something that allows you to run your LPC8xx code unchanged as this code is going to be accessing the peripherals directly and this is not normally possible in Linux (you access peripherals through drivers, but this can make the coding much simpler). Also your code would probably run as a task (or tasks) under Linux.
Next, what is the structure of the code. Is it just a simple loop, does it use interrupts, is it using an RTOS etc? Does it have hard real-time requirements (hard real-time is not normally possible in standard Linux)
What peripherals and other features of the LPC8xx are you using/are required.
Have you considered attaching your existing LPC8xx design to a Linux system, perhaps using a UART, SPI, USB?
Without know your exact requirements it is difficult to give a definitive answer.
