Yes, you are right. It should be 'needs' or 'should need'. There are cases where 'need' can appear without the third person 's', but only when it is being used as a modal verb followed by another verb.

Technically it is correct if we consider "need" as present subjunctive. However, the reality is that we wouldn't ever use that form unless we wanted to sound archaic or formal. "Should need" is an option, and saves us the confusion of re-interpreting the sentence. For 99.99% of the time, we'd say "If she needs it, I will lend her the money."

If you use "he", "she" or "it" then you have to add the "s" to the verb. "She needs it."

Needs