Answer:
The sentence would be as follows: The scientist's theory, as well as his ideas, lack support. Other scientists do not agree with him. The verbs that correctly complete the sentence are lack, and do.
Explanation:
In the first sentence, two elements that do not have enough support are mentioned: The scientist's theory and his ideas. Therefore, the verb following this NP subject should be plural (lack). Then, the subject of the second sentence is also plural as its noun head is scientists. Consequently, the verb following said NP should also be plural (do).
