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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.
It's possible, if a little tautological. 'Escalate' already implies upwards movement, but then again, Westlife had a hit with a chorus that went: "You raise me up..."
We often lift things up when "lift" alone would presumably suffice.