ln Arabic language, if any verb comes after the negative particle (لَــمْ), then this verb has to be present tense, even the whole sentence is telling about past tense. So the most accurate writing is :
.لكنه لـَمْ يَفتح الباب
Hint : there are another negative particles, they have a simple differences between each other.
if you need more explanation with examples, please don't be shy to ask for help.