"She does not have a lion in her house."
Translation:لَيْسَ عِنْدها أَسَد في بَيْتها.
No, because the construction is completely different in Arabic. In order to express the verb to have in Arabic, we literally say "this thing is (not) to this person". Therefore, here the verb لَيْسَ has to agree with the subject which is lion = أَسَد in Arabic.