I agree with
Jim Thompson's post about your problem, but I'm not sure about the replacement prices.
Here is where you can find the
John Deere parts and prices.
When you enter your model number, use LX279 without the space!
A JD replacement for your fuel pump appears to be $129. I couldn't find a separate price for just the diaphragm.
You may find some 3rd-party replacement parts much cheaper at other places. Look up the part on the John Deere site, then Google the part number. Be aware that the 3rd-party replacement part may not be quite the same quality as a genuine John Deere part.