I'm not comfortable with my mom wanting me to lie to my grandfather
You've gotten close to this in telling your mom you're uncomfortable, which is promising. You just need to nudge it to "no."
Just like integrity itself, though, this issue isn't without nuance. It's fine to assure her you won't go around volunteering information to people; you don't have to be proactively truthful. Just make it clear that when asked, you won't respond with a lie.
When it's realistic to, you can also defer questions to her. Presumably you know when and how your grandfather tends to ask things. That means you can be ready with the most logical phrasing of, "You need to ask my mom." I could argue that's the familial equivalent of suborning perjury; however, it also counts as good emotional hygiene to decline invitations to get in the middle of other people's power struggles. Your grandfather quite possibly asks you because he knows you're more forthcoming than your mom, and that's as underhanded as your mother's dishonesty. You owe no apologies for opting out of their dysfunction.
If I had to guess, I'd say your mother cultivated her deception skills as a defense mechanism -- an unhealthy one, obviously -- against the paternal guilt-tripping, which itself was probably an unhealthy defense mechanism for some emotional tendency in his family, and so on.
If this is indeed a family pattern, then breaking it will be hard work, but worth it. Consider talking to a good family therapist if the family's dysfunction or your discomfort with it runs wider and deeper than this.
Standing by your own decisions even under the worst familial pressure feels better than making things up to appease others, because the former is the act of an adult and the latter the act of a child. Trust that.
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