Is the word "lukaa'ah," uttered in a low voice while waiting for a relative to finish praying, considered mockery that leads to disbelief (kufr), especially with the recurring feeling of doubt and renewing one's Islam for fear of disbelief?

One should use the best of words. The phrase "Ya Satir" (O Coverer/Protector) has no relation to disbelief (kufr), nor does it indicate mockery or denigration of the Sharia (definition). Rather, it is a complaint about the delay in an answer. Its speaker is not considered a disbeliever due to the absence of any evidence for deeming it an act of disbelief or for the speaker's heart being content with disbelief. It is advisable to supplicate, humble oneself in prayer, distract oneself from intrusive thoughts (waswās), and consult a psychiatrist.