«وَلَا تُجَشِّمُوا لِأَجْلِي أَكْلًا»
And do not put yourselves through the trouble of preparing food solely for my sake.
The guest asks hosts not to trouble themselves over a meal for his sake. Li-ajlī specifies the reason, and the wording projects courtesy and restraint.
Courtesy of expression is an observable speech act, not a comprehensive guarantee of the guest’s future behaviour. The full episode, rather than a single polite sentence, determines his characterization.
Applied question
What relation does li-ajlī express?