Thank you very much for your focus on Freescale Kinetis product. I am glad to provide service for you.
I've had a go through the KL02's RM and it says the LPTMR interrupt can be used to generate a wakeup from any low-power mode, including the low-leakage modes.
I'd like to suggest that you can through the link below to download the FRDM-KL02's demo code which include a lowpower mode code. Wish my support can support.
Thank you for your post, however please consider moving it to the right community place (e.g. Kinetis Microcontrollers ) to get it visible for active members.