No state's capital name contains the word lake.
There are 3 syllables in the word "capital".
The word state is not a proper noun by iself.
Not necessarily. Capital is a more broad term, just referring to the capital of any place. It could be a country, state, province, organization, etc. State capital is more specific, referring to the capital of a state.
Dover
Capitale for a State - Capoluogo for a region
The word capital is derived from the Latin word caput, which means head. So a capital city is literally the head city of a state or nation.
The anagram is Springfield, the capital of the state of Illinois.
The anagram is Augusta, the capital of the state of Maine.
The anagram is Jackson, the capital of the state of Mississippi.
The anagram is Helena, the capital of the state of Montana.
The anagram is Olympia, the capital of Washington State.