Player characters normally have an attunement limit of 3 items.
As a warlock, if I have a weapon that normally requires attunement, will it still take up one of my attunement slots after I make it my Pact Weapon?
Yes, it still takes up an attunement slot.
There are no rules in the Pact of the Blade Warlock section to suggest otherwise.
If a weapon normally requires attunement in order to gain full use of its features this will not change when it is made a pact weapon.
The rules around transforming another weapon into your pact weapon are as follows:
You can transform one magic weapon into your pact weapon by performing a special ritual while you hold the weapon. You perform the ritual over the course of 1 hour, which can be done during a short rest. You can then dismiss the weapon, shunting it into an extradimensional space, and it appears whenever you create your pact weapon thereafter. You can’t affect an artifact or a sentient weapon in this way. The weapon ceases being your pact weapon if you die, if you perform the 1-hour ritual on a different weapon, or if you use a 1-hour ritual to break your bond to it. The weapon appears at your feet if it is in the extradimensional space when the bond breaks.
No mention is made of attunement changing in any way, when a weapon becomes a pact weapon, therefore it doesn't.
The eldritch invocation Improved Pact Weapon from XGTE, doesn't affect attunement either.
It is, however, always possible to wield a weapon that requires attunement without attuning to it, you just won't benefit from any of its features that require attunement. A sword you haven't attuned to in order to deal extra fire damage is still a sword you can wield like any other sword.
To provide a thought to clarify how this works: Your attunement is for the powers of the magic item itself. Making something your pact weapon applies the effects of a pact weapon to a weapon. Neither of these elements interacts with the other, so both function as written without modification.