In the following sentence:
昨天晚上买了张彩票，结果中奖了。
If I understand it correctly, 张 means 一张 but 一 is omitted here.
Also, if you want to mean it in plural (i.e. buy multiple lottery tickets), the sentence should be the following.
昨天晚上买了些彩票，结果中奖了。
Now, can I also omit 张 as well, to make the sentence the following:
昨天晚上买了彩票，结果中奖了。
In this case, does the sentence mean singular, plural, or both (which makes the meaning dependent on context)? Or is the sentence invalid grammartically in the first place?
In my understanding, if you omit 张 as well then you only focus on the latter part, which is 中奖了. It won't make a turning point that obvious.
If you add the 张 or 些, however, you not only focus on 中奖, but the tickets play an important role as well. It's kinda like when you say "tickets" and "the tickets."
Omitting 张 is more like when you are telling things calmly. For example, 我昨天买了彩票、啤酒、炸鸡。 You don't need to focus on anything. But if you say 我昨天买了瓶啤酒, then others would expect you tell something about it -- or it's related to the context.
But you are right, it's grammatically correct though.
“昨天晚上买了（一）张彩票，结果中奖了。”，it indicates you buy One ticket. You'd better use 几张 to indicate that you bought several tickets. I am not saying you are wrong by 买了些彩票, but in practice, 些 is often used to describe uncountable nouns. For example, 我买了一些水果。这些事情。说些什么？
you can say '昨天晚上买了彩票', which conveys the fact/behavior itself you bought some/a lottery ticket(s) (how many you bought is not the point/important; Or you deliberately don't want to tell how many you bought; Or people don't care the number of tickets you bought.)
