Could lexapro (escitalopram) cause blood pressure spikes?

No : Lexapro (escitalopram) doesn't affect bp. In rare instances, it can be associated with the serotonin syndrome which can cause rapid heart beat associated with agitation and twitching (neuromuscular irritability/hyperreflexia).

Possible: Yes it can happen. However, it's a good idea to get checked by your primary care physician to make sure other causes are looked at as well.