I adored my grandmother but there certainly was a stage in my life, late teens and early twenties, when I was very lax in seeing her or replying to anything! I got better and started spending more time, staying for the weekend etc. I was heartbroken when she died when I was 36.
I think that you are upset about the lies ...... but saying that a card is on its way is more omission than fiendish lie, and the good old ‘lost in the post’ is shorthand for (in my case anyway) I bought a card, and it’s here somewhere, and I love you and when I get a moment and when I get a stamp .... !
You have had some wonderful suggestions from other people on this post, but in my opinion, do keep it light, don’t (appear to) nag and keep cool about it all, if you can. ?