Which expedition, led by Mirabeau Lamar, aimed to annex New Mexico to Texas but resulted in failure?

The correct choice is the Santa Fe Expedition, which was led by Mirabeau Lamar in 1841. This expedition was motivated by Lamar's desire to expand Texas territory and annex New Mexico, reflecting the broader ambition of Manifest Destiny during that period. The expedition consisted of a military attempt to seize control of Santa Fe but faced numerous challenges, including logistical issues, lack of support, and resistance from local forces. Ultimately, it resulted in a retreat and significant losses, marking it as a notable failure in Texas military history.

The other options represent different events or military campaigns in Texas history that do not pertain to Lamar's expedition aimed at New Mexico. The Mier Expedition, for example, occurred later and was focused on a raid into Mexico rather than on annexing territory. The Archive War was primarily an internal conflict relating to the preservation of government documents and did not involve military expansion. The Rio Grande Patrol was more concerned with law enforcement and border issues rather than territorial annexation. Understanding these contexts helps clarify why the Santa Fe Expedition is specifically associated with Lamar's aims and subsequent failure.