Hi
Brief answer:
No , lexapro does not cause neck 
stiffness and pain.
Detailed answer:
I had gone through the question and understand your concern.
See , lexapro does not causes neck stiffness and pain , as these are totally unrelated side effects.
However , the common side effects of lexapro are
   1. 
drowsiness, dizziness;
   2. sleep problems (insomnia);
   3. mild nausea, gas, 
heartburn, upset stomach, constipation;
   4. weight changes;
   5. decreased sex drive, 
impotence, or difficulty having an orgasm; or.
   6. 
dry mouth, yawning, ringing in your ears.
I hope this information helps.
Let me know if you have any other queries.
Thank you.