1) While OTL Texas does lack iron, coal, etc. it does have oil and cattle. The latter would be a great reason for Britain to take a constructive hand in investing in the young Lone Star Republic. (In OTL, most ranches were backed by British financing).
2) The Texas outlined in the map does include substantial mineral deposits in what is OTL Northern Mexico.
3) They could have cotton/textile industries, chemical industries (sulfur deposits). The Rio Grande valley is quite fertile and is farm country today. There's no need for Texas to necessarily have a huge arms industry to be big country unless it's planning to fight other such countries. Only the US might be such a contender. In a scenario where it remains independent, Texas might have remained isolationist enough that war simply wasn't a factor in the 19th century: it took enough to fight off the Indians and earn a living.)
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A few more potential PODs that could yield such a Texas:
1) Santa Anna returns to Mexico and recognizes the Treaty of Velasco, leaving Texas free from the necessity to resist Mexican invasions in the early 1840s, which bankrupted the nation. A similar vein, Santa Anna does not rise to power again in 1842 and Mexico descends into civil war, similarly leaving Texas free from the need to bankrupt itself.
2) The Texians manage to coordinate their revolt with the ongoing Liberal revolt against Santa Anna's conservative coup. The Yucatan wins its independence (in OTL it was recognized by Great Britain). The Republic of the Rio Grande aligns with Texas. This wider war drags on for longer than the Texas War of Independence did in OTL, and eventually Texas enacts some form of emancipation/manumission in order to increase the size of its armies. This prompts Great Britain to give even more support to the fledgling Republic.
The really interesting question here is whether Texas really becomes independent or the Mexican Liberal re-institute the Constitution of 1824 with Texas as separate state from Coahuila--Texas' original demands in its revolt. It could easily happen that Santa Anna is not absolutely defeated and the Yucatan is made a free state, and Texas/RGR merge into Texas. Then the US buys California at some point. (Or maybe Texas does, once they find oil and have the money to do so.) Or maybe Great Britain intervenes in the French attempt to impose Maximilian in the 1860s (because they supported a Monroe Doctrine-like policy with regards the Western Hemisphere, dating from Canning's ministry in the 1820s); they force Mexico to cede more land to Texas, supporting it for the same reasons they would invest in Argentina.