"I do not understand the lecture."
Translation:Я не понимаю лекцию.
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"Лекций" is plural genitive. Singular genitive would be "лекции". You could say "я не понимаю лекции" but that sounds a bit old fashioned. Not all negative sentences require the genitive case. Expressions like "there's no X" and "I don't have X" do require it, but in instances like "I don't understand X", "I don't see X", "I don't want X" and so on, the genitive is optional and, as I said, slightly dated. It's a slow process but the accusative is replacing it in such situations in modern Russian.
You can omit it without losing the meaning, but it's less common among native speakers. We tend to keep the pronouns in such sentences (but at the same time we tend to avoid repeating the same pronoun too often, so if you have already used "я" in a previous sentence/clause it would be more acceptable to drop it here)
It's not wrong but it's not neutral either. It suggests some kind of emphasis or emotion. For example if you were really exasperated, or if you wanted to stress the "я" ("don't know about you, guys, but I don't understand it"), or something else, depending on your tone and the context.
If you say it in a neutral tone it would simply sound weird.