When to capitalize words such as "lake", and when can the whole word be omitted?

Which of the following sentences are correct?

"He gave two examples of large lakes, Lake Michigan and Lake Superior."

"He gave two examples of large lakes, Michigan and Superior."

"He gave two examples of large Lakes, Michigan and Superior."

"He gave two examples of large lakes, Lakes Michigan and Superior."

This question is primarily about what variants are formally correct, not which one sounds the best.

I think that the question should be valid for several words of the same kind, such as mountain (Mount), figure (Figure), table (Table) and so on.

You capitalize it when it is used as part of a proper noun. Your first, second, and fourth examples are correct, the third is not.

He gave two examples of large lakes, Michigan and Superior.

In this example, the Lake part in the proper nouns Lake Michigan and Lake Superior is omitted. The word lakes here is not part of a proper noun. So capitalizing it like this,

He gave two examples of large Lakes, Michigan and Superior.

Is incorrect.

In other cases, the same rule applies: capitalize the words when they appear as part of a proper noun, such as Mount McKinley or Round Table, but not when they appear as common noun, such as the tallest mount/mountain or coffee table.

It is also recommended to capitalize references to specific figures, tables, chapters, sections, equations—particularly when they appear with a number or letter identifying them:

This trend is demonstrated in Figure 5 in Appendix C

But again, not when simply using the common noun.

This trend is demonstrated in figure below.