Saul鈥檚 and David鈥檚 parting of the ways is not known to others yet, so David is able to lie about what he is doing. David鈥檚 lying will lead to murder in the next chapter. To be protected from Saul, David goes to Philistine territory in Gath. Saul can鈥檛 pursue him there because it would look like an invasion and start a war.
This is a story Jesus refers to in Matthew 12:3 and 4. Jesus is questioned about his followers picking grain on the Sabbath, a holy day of rest. Jesus points out that meeting the greater need for food is more important than a ceremonial rule. It鈥檚 easy to get our priorities backwards sometimes. The temptation is to value a rule over a person. Rules matter, but people matter more. We should wisely apply rules for the maximum benefit of the people the rules were designed to protect.