Yes, it should be capitalized.
The area of Lake Allatoona is 48.603 square kilometers.
Lake Allatoona
Yes, it is referencing a specific lake, so Lake Michigan is correct.
Water, fishing, hydroelectricity, recreation, controlling flooding, and perserving wildlife.
Lake House is a noun clause Lake modifies House, both components should be capitalized.
From Rivers Lakes Groundwater And Under ground caves
Lake would not be capitalized unless it begins a sentence, as in this sentence. Or if it is part of the name of a lake such as the Great Lakes.
Capitalize Salt Lake. You do not have to capitalize county criminal justice system.
Battle of Allatoona happened on 1864-10-05.
Allatoona High School was created in 2008.
All lakes in Georgia are man made. This does not include the swamp in south Georgia which are natural, protected wet lands.
Have should be capitalized if it is the beginning of a sentence. Summer should not be capitalized.