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Lift is different. Ordinarily it implies up but it can also be used in the sense of lift over which does not imply any alteration in ultimate elevation. Escalate though is unidirectional meaning to move up. It is evolving to mean increase, as in the fire's intensity has escalated, although that would seem to have developed from a contraction of the fire's level has escalated; ie moved up a scale of measurement.
Is it possible to 'escalate that up '?
I will ask that question and have that conversation.