Final answer:
Lamar might fear the loss of fundamental rights such as free speech, bearing arms, habeas corpus, and protection against cruel punishment if Texas's independence were surrendered, as these rights are enshrined in the U.S. Constitution and are considered essential to liberty.
Step-by-step explanation:
When referring to the rights that Lamar might fear losing if Texas's independence were surrendered, we would consider those fundamental liberties associated with the American understanding of constitutional governance and the Bill of Rights. These rights include the right to free speech, which allows individuals to express themselves without government restraint; the right to keep and bear arms, which permits citizens to own and carry weapons for self-defense; provisions for the right to a writ of habeas corpus, safeguarding against unlawful and indefinite imprisonment without due process; and the protection from cruel and unusual punishment, which sets limits on the penalties that the government can impose.
Thus, the invaluable rights that Lamar might be referring to include various civil liberties that are deeply ingrained into the American constitutional fabric. These are rights that are broadly recognized and protected under the U.S. Constitution, such as the freedoms of religion and speech; the right to assemble and petition the government; the right to a free press; and the fundamental protections provided by the legal system against unjust prosecution, which collectively ensure the blessings of liberty as outlined in seminal documents like the Declaration of Independence and influenced by natural rights philosophy