Air carrier pilot reported the NOTOC was missing a Lithium Battery contained in equipment. After collaboration with Load Planners and FOM research the pilot requested and received an addendum to the NOTOC to make document legal and allow the flight to depart.

Narrative

During the completion of the preflight of the flight; ZZZ to ZZZ1; I was reviewing the NOTOC and noted the Aircraft DG (Dangerous Goods) Loading Summary noted 0 UN3480 and 0 UN3090 Lithium Batteries. Proceeding onto page 2; I noted there was 1.2 KG of UN3091 Lithium Batteries contained in equipment. I inquired the Load Supervisor why it was not reflected. Load Supervisor left and checked with the ZZZ Load Planners and returned to state they tried to change the summary amount but the program would not allow the number in the summary to be changed. While the Supervisor was away; we referenced our company manual. I do note a section of the company manual referenced only UN3480 and UN3090 and the Summary only lists those two items. However; Lithium Battery Mark; stating in the note at the bottom of the page; Those Lithium battery shipments bearing the Class 9 label will be on the NOTOC. All other lithium battery shipments will not be listed on the NOTOC. The two UN3091 items were listed and thus accompanied by a Lithium Battery Mark. The ICAO Doc 9481; notes the UN No 3091 is Lithium metal batteries contained in equipment and has the exact same drill code as 3090. I asked the Load Sup to have the ZZZ Load Planners to contact ZZZ1 Load Planners to determine if this is a legal and acceptable NOTOC due to the fact; if we have an emergency and the Fire Chief looks at the NOTOC quickly; the Fire Chief will assume there is negligible amounts or zero of lithium batteries on board. However; we have 1.2 KG of Lithium and enough to have two separate entries in the items on page two of the NOTOC. Additionally; I called the dispatcher and notified him of the situation and to work with load planning to ensure the form was legal and acceptable. ZZZ Load Planning stated ZZZ1 could not change the summary as well. I never received an answer but the Load Supervisor on the aircraft found the ULD (Unit Load Device) Summary. I informed the Load Sup if they can get a copy and sign both supplemental forms to certify the load is legitimate and staple to the front of the NOTOC as a supplementary document in cases of emergency; I would be comfortable (and asked the FO (First Officer) who was also). The ZZZ Load Supervisor was able to make a copy and attach to the two NOTOC packages. We then completed the Load Manifest procedures per the AOM and departed without further issues. Upon further research I would like to know; does the Summary UN3090 include subcategories (e.g. 3091); and if no; why not; as they have the same drill code and response. Recommend they are included.