No, you shouldn't; lying is wrong, and in the long run it would solve nothing. The Bible is clear: "Each of you must put off falsehood and speak truthfully to his neighbor" (Ephesians 4:25).
What you should do instead is ask God to help you be a peacemaker when you get together with relatives this Christmas. After all, the Bible calls Christ the "Prince of Peace" (Isaiah 9:6), and when you gather on Christmas you should be seeking to honor Him. Yes, some of your relatives may be difficult–but can you honestly say you've done all you could to bring peace to your gatherings?
How can you do this? First, ask God to help you refrain from topics that are likely to cause argument. The Bible says, "Without wood a fire goes out; without gossip a quarrel dies down" (Proverbs 26:20). If those subjects come up, gently but firmly refuse to participate in any discussion. Instead, come prepared with a list of neutral topics–what others did on vacation, for example.
Most of all, ask God to help you focus on Christ and His goodness to you as a family. Pause to thank God for your food before the meal begins, and share with others what He has done for you during the last year. God loves your family–and with His help you can, too.