Choose the particle by the relationship between the two parts of the sentence.
Particle
Core meaning
Recognition
كَيْ / لِكَيْ
so that; purpose
states the purpose of an earlier action
إِذَنْ
then; result or reaction
responds to a complete preceding statement
حَتَّى
until; endpoint
marks the point up to which something continues
لِ
in order to; purpose
joins the imperfect and states purpose
The table compares meanings only. The complete sentence still determines the intended relationship.