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This first paragraph is conjecture, based on what I've read of the history
of Texas, I surmise that the "Lonestar" is symbolic of the fact that Texas
rebeled from Mexico and fought and won its war of independence without
assistance from the United States or any of the original colonies. The
Texicans asked for but did not recieve assistance from the United States,
until after Texas defeated Mexico. Where the red, white and blue flag of
the United States had thirteen stars on a field of blue, and thirteen red
stripes symbolizing the original 13 colonies; the red, white and blue Texas
flag was chosen to have one star and one red stripe. Texas achieved its
independence without help from any other government, and the "Lonestar" is
symbolic of that achievement.

The following is historic fact:

On March 2, 1836 (Texas Independence Day) a convention of Texicans met at
Washington on the Brazos, declared independence from Mexico and formed the
Republic of Texas. Ten days later the convention adopted "a single star of
five points" as the "peculiar emblem" or symbol of the Republic of Texas.
Nine months later they incorporated this symbol into the seal of the
Republic of Texas and in 1839 it was incorporated into the national flag of
the Republic of Texas.

When the Republic of Texas accepted annexation into the United States in
1846, the design of the seal and the flag was retained, changing only the
word "Republic" to "State".

Adding to the mystique of the "Lonestar" was its adoption as the badge of
the Texas Rangers, the form of the badge is a Lonestar inside of a circle.
The Texas Rangers were originally formed in 1823 as a home guard to protect
against Indian raids and pursue criminals. The oldest authenticated Ranger
badge was made in the 1880s.