Here papel can be translated as napkin. In fact, this sentence would be better if you use the word servilleta that is a square piece of cloth or paper used at a meal to wipe the fingers or lips. On the other hand, necesito is the conjugation of the verb necesitar for the first person singular in the simple present. Finally:
<em>Necesito papel para </em><em>el almuerzo</em>
It's also valid:
<em>Necesito </em><em>servilleta</em><em> para el almuerzo</em>
<em>Necesito </em><em>servilletas</em><em> para el almuerzo</em>