The final vowel in words such as "happy" can either tense or lax - it really doesn't matter. In the past, RP speakers tended to use a lax 'i' in these words. If you listen to English voices from before the 1980s, you'll hear a lax 'i', whereas nowadays most people tend to use a tense one.

I'll add to SuKi's on-point answer, as the vowel at the end of “happy” is actually quite interesting. It doesn’t have primary or secondary stress — it is completely unaccented. In English, most vowels are reduced to the schwa (/ə/) when entirely unstressed, but there are some exceptions. Although the tense /i/ is not reduced completely to a schwa, it is shortened compared to how it would be pronounced in an accented syllable. I believe native speakers usually perceive the tense /i/ in happy as being the same as the vowel in “key,” but it isn’t really. Compare: happy: /ˈhæpi/ key: /ˈkiː/ (long /i/) or diphthongized (American style) /kɪi̯/ This reduction is typical in English when /iː/ is unaccented at the end of a word. For example “Does he like cheese?” /dəziˌlaikˈtʃiːz/ The vowel in “he” (despite the fact that it’s in an open syllable) is noticeably shorter than the first vowel in “cheese.”