The Memory View with the LPCXpresso IDE provides easy to use options for exporting the contents of target MCU memory back to the computer running the debugger, and similarly to import into the target MCU's memory.
To export an area of target memory, go the the Memory View (ensuring the "Traditional" rendering is displayed) and select the Export icon...
This will then display a dialog allowing you to select the location and size of the memory to export, as well as the format to save the file in (text, binary or SREC)...
In the same way, you can use the "Import" icon to allow a memory to be written to. Note that this does not allow Flash memory to be programmed.
It is also possible to save the contents of memory out from the command line, or from the gdb windows within the IDE, using the 'dump' command.
Alternatively, you may be able to use your MCU's ISP mode to transfer using FlashMagic.