I believe your native Cantonese has both sounds, so you’re probably just asking about the spelling rule in Hanyu pinyin. If the ü sound (IPA /y/) is after L or N, then it is written with the two dots (umlaut): lü, nü. If you don’t have the ü symbol, you could theoretically use the letter V instead (lv, nv).
However, if the ü sound comes after a palatal consonant (y, x, q, j), then the umlaut is unwritten, since palatal consonants can only be followed by /y/ or /i/, never /u/. So, yu, xu, qu, and ju are all pronounced with the ü sound, even thought the two dots are not written.