In general: players in D&D shouldn't be limited by lore restrictions. A male cleric of Lolth is an oddity, but so are all player characters. They're the heroes. As a DM, when someone says they want to do something like this, the answer is not "you can't", it's "okay, and this is what that will entail..."
To a certain extent I would agree. But the fact cleric powers are bestowed by a goddess, we could say that if one of her tenets specifies clerics should only be females, and you would allow a male cleric in your D&D campaign, it would entail one of these three principles:
1) Menzoberranzan priestesses are liars who hide to the males the fact they could, if they so wanted, become priests of Lolth, thus no such tenet exists.
2) In your campaign, the character has done a special and exceptional deed lore wise which would have allowed him to become a priest of Lolth.
3) You don't care about the drow lore at all and you do what you want as a DM with your campaign.
Everyone of them is perfectly fine, but the latter is kind of problematic with a game which advertises it follows the D&D 5e lore and rules.