这个句子应该是：the Lecture Room program. 句中gain 用复数，说明主语是Yu Dan 和 the Lecture Room program 是两个部分。如果gain用单数，那么主语应该改为：The Yu Dan and Lecture Room program. 如果单独使用Lecture Room，作为名称，不用冠词。

initiative 可以是形容词。你可查the free dictionary 便可知。

附上一个外媒例句供你参考：

In late 2006, a series of her lectures entitled "Yu Dan's Insights into the Analects" was broadcast for seven days on China Central Television (CCTV) as part of the Lecture Room program.