In the Musaf of Rosh chodesh, we say, ראשי תולדותם לכל כפרה זמן נתת לעמך חדשים, "You gave Rosh chodesh to Your nation, a forgiveness for all their תולדות." The Beis Yosef (Tur 423) writes that תולדותם means deeds. Rosh Chodesh atones for all the bad deeds we might commit throughout the coming month, שונא מיד נפשם תשועת, "to save their souls from the enemy." The enemy is the yetzer hara. In the merit of Rosh Chodesh, Hashem saves us from our enemy, the yetzer hara.
Hashem promised Avraham that (Bereishis 15:15) טובה בשיבה תקבר, that he will be buried at an old age. Reb Shamshon Ostropoler zt'l (in his commentary on sefer Karnayim 6:1) says that the first letters of ובהט שיבהב קברת spell ת"טב. Hashem hinted to Avraham Avinu that he will be niftar on Rosh Chodesh Teves. There are three great merits and kedushos on this day. It is Chanukah, it is Rosh Chodesh, and it carries the merits of Avraham Avinu, too, because it is his yahrtzeit.
Avraham davened for Sedom, but the cities were overturned. Lot davened for Tzoar, and it was saved. We can explain, b'derech tzachus, that this is because Lot began his tefillos by praising Hashem. He said in his tefillah (Bereishis 19:19) עבדך מצא נא הנה נפשי את להחיות עמדי עשית אשר חסדך ותגדל בעיניך חן, "See now, Your servant has found favor in Your eyes, and Your kindness was great which You did with me to save my life..." After this praise, Lot prayed that Hashem save Tzoar, and Hashem accepted his tefillos. This is because a tefillah that is said amidst praise is a very powerful tefillah.
Let’s use this auspicious time of Chanukah when we praise Hashem to also ask Him for all our needs.