It stood alone. There were valid reasons why the US could not and would not actively support the Texas Revolution from Mexico. The following are a few examples:
The nickname is in reference to the state flag.
Texas
Texas adopted the nickname of lone star republic
Perhaps you mean a "Lone star" rather than a "long star." The Lone Star State is another name for Texas. Texas adopted the term "the Lone Star State" in the mid 1830s, after breaking away from Mexico. And for the period between her separation from Mexico and its becoming a state it was named the lone star republic.
the lone star republic
Texas
the Lone Star Republic
Texas
It was known as the Republic of Texas. Its nickname was "The Lone Star Republic", and it is still known as "The Lone Star State."
Texas is known as the Lone Star State.
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Mirabeau B. Lamar
Lone Star
Dwight D. Eisenhower