Welcome to JA,
My Name is John.
The lamp reset is a pain on this set but here is the process:
go to the TV and press and hold down the volume DOWN button ON THE TV (not the remote). While pressing and holding the Vol down, press and hold the SPLIT key on the remote for 5 to 10 seconds (make sure that the remote is pointed at the remote recieve which can be awkward to do with 1 person so if you can get help it might be easier).
That is right from the panasonic service manual for your set so that should work if it doesnt i can drop an email to my tech rep and see if they can provide a clear answer to your problem.
Let me know if this does not resolve the issue.
If you have any questions please ask.
This set requires the Split button to reset the timer, the only other way to reset the timer is to force the set into factory reset through the service menu but that is never recommend because it can screw up the sets alignment which is very hard to setup with out the factory tools.The original i posted a picture of below it is a must to reset the timer the part number for the remote sold for this set: eur7627z70
Here is a blown up image of the button that needs to be pressed:
If you do not have this remote can you please post a picture of the remote you do have by using the tree icon in the toolbar.
Hope this helps.
The problem is you have the wrong remote, no other good way of saying per the parts list and every website i have found that sells that model the pt52lcx15 B/k and standard model all use the same remote.
You need that original you need to contact the dealer that sold you that set, i can not imagine that remote was the original provided with the set, it had to be open boxed or otherwise and if they sold it not being open box they had to have broken some laws by not disclosing the set sold open box, if it was sold at costco contact the coinciege service and they will ship you a remote at no charge as long as the set is under 2 years and even if it is not fight them on this because it is the wrong remote you have to have the split button to clear the counter without damaging the set.
If you can not get the original you can order an after market that has the split button preprogramed like remotes.com http://remotes.com/remotes/servlet/rs?a=Search&o=c&uid=0&m=pt52lcx15&uuid=12509156672780
The original can be ordered from panasonic directly for around $50 but i have found many on ebay and some on craigslist that are sold as used for around $10-30.
If the picture you provided is the remote you have you can not reset the lamp timer because the remote is not designed for that model of set.