Ever since I learned that "if" and "when" can be used as translations for the -たら conditional form depending on the context, I have been looking for an explanation of its construction in terms of its etymology to have a proper understanding of how it works. The sources I have looked up say that it is formed from the "past tense" -た form + ら, but I have failed to find any information on this ら. Is it a classical Japanese auxiliary verb? Is the full form -たらば? Does it have anything to do with the 連体形 or attributive form of classical verb ending ～たり? Or is -たら the 仮定形 form of -た?
Please enlighten me on this topic so that I can stop translating this expression to English and start seeing it in terms of Japanese.