Can you use mana from a Gilded Lotus to pay for its own equip cost?

Gilded Lotus is an artifact but it is not an Equipment. It has no equip ability and therefore has no equip cost. The question as literally stated has no practical scenario: you cannot pay an equip cost that doesn't exist on Gilded Lotus (CR 301.5).

If the real question is whether you can tap Gilded Lotus to add mana and then use that mana to pay the equip cost of a different Equipment, the answer is yes. Mana added to your mana pool stays there until the step or phase ends (CR 106.4), so you can absolutely tap Gilded Lotus for {3} mana and immediately activate an equip ability with that mana.

Equip is an activated ability with a cost that includes mana (CR 702.6a). Activating it simply requires you to have the mana available at the time you pay costs (CR 602.2). Gilded Lotus's mana is perfectly legal to use for this purpose.

Example: You control Gilded Lotus and a Sword of Fire and Ice equipped to nothing. You tap Gilded Lotus for {U}{U}{U}, then activate Sword of Fire and Ice's equip ability by paying {2} from that mana pool, choosing a creature. The equip resolves and the Sword becomes attached to that creature.

There is no rule preventing you from using mana generated by one permanent to pay costs of an activated ability on a completely different permanent, so this works cleanly.