I always thought that letse -- as in the "letse ka!" vulgarity we love to use in the Philippines -- is derived from Spanish. After all, letse... leche... 333 years of Spanish occupation... just made sense. But then I heard of the Bahasa Melayu word leceh which is used exactly the way we use letse, and it got me rethinking my hypothesis. I am now inclined to think we got it from our Malayo-Austronesian roots rather than Spanish. Let me explain.
Leche as a cuss word, I understand, is practically unheard of in modern Spain or Latin America. It's milk, and you're more likely to hear it in the context of desserts rather than their digested byproduct. Closest uses of leche as an expression I could find are me cago en la leche and con mala leche, which are used more like exasperations or idiomatic expressions.
The Malay leceh, on the other hand, is an accusative or insult directed at a person or situation. Meaning troublesome or annoying, leceh requires an object and is used in almost the exact same context we use letse.
This will need more research and confirmation, but I am now inclined to think that letse is a pre-Hispanic cuss word. It may be more related to leceh than leche. Amazing how inverting two letters can change the entire history of this cuss word.