Today is day 6 at my new job, but I got a job offer elsewhere I want more

So I left my old job on March 15, and started this new job (Company X) on the 25th.

Today at lunch Company Z called me up, and made me a better offer which I already accepted. Tentative start-date on April 15th...

But now what do I tell Company X to make this the least amount of awkward? My dad suggested I create a massive fib, that I need to tend to my sick parent out of state for a few months. Tell them I want to come back, but that family comes first. He thinks this will give me some buffer in case Company Z doesn't work out, so I can return. BUT-- I have my doubts that it's worth it because 1. I am a bad liar and 2. I doubt I would ever be welcomed back regardless.

Also, should I just quit right now? Or wait a couple days to soak up more on my one and only paycheck?

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