The Talmud teaches that Hashem did not ‘need’ the light of the Menorah. Rather, the light of the Menorah served as a testimony to the entire world that Hashem’s presence rests amongst the Jewish people.
More specifically, the testimony was the miraculous ‘western lamp’ (נר מערבי). The other candles of the Menorah only burned through the night. Even though the ‘western lamp’ contained the same amount of oil, it would burn through the day as well. The Kohen would use it to light the other candles that evening.
According to the view that the Menorah stood facing from east to west, it would seem that the ‘western lamp’ refers to the western-most lamp; the one closest to the Holy of Holies.
However, the commentaries explain that the ‘western lamp’ was actually the 2nd lamp from the East. It is called the ‘western lamp’ because it was the first lamp towards the West.
The 7 branches of the Menorah represent the 7 emotional drives of the soul, which parallel the 7 Divine energies of the Sefiros. These give rise to 7 different ways in which we serve Hashem; love (Chessed), discipline (Gevurah) etc.
The western-most flame corresponds to the first Sefira - Chessed (love and kindness). The 6th candle corresponds to the attribute of Yesod and the 7th candle corresponds to the attribute of Malchus. Yesod is Hiskashrus – a deep bonding and intimate connection with Hashem. Malchus is humility.
So, the unique ‘western lamp’ is Yesod. It is used to light the others because Yesod – a deep intimate connection with Hashem – is the source that ignites and leads to all of the other specific modes of serving Hashem.
The Torah describes this lamp as being ‘before Hashem’ (the Divine presence that rested in the Holy of Holies which was to the West). This is because the intimate connection of Yesod places us face-to-face before Hashem.
But the 6th lamp is only the ‘western lamp’ because it sits to the west of the 7th flame. Whilst the primary aspect of serving Hashem is our Hiskashrus, one cannot attain this deep connection (Yesod) without first having humility (Malchus).
~ Based on Reshimas Hamenorah and Igros Kodesh Volume 3 p229