Before You Begin
“My Master, Open my Lips, and my Mouth will Relate Your Praise.”
The Sages instituted the recital of this verse from Psalms at the outset of the Shemone Esrei to help remind the worshiper that speaking to G-d is a very serious matter. Ideally, one should pause momentarily before beginning his prayers so as to properly focus one’s thoughts and emotions on what he is saying. Since its function is to help enhance the quality of one's prayers it is considered as part of the prayer itself, and is therefore not considered an interruption (Levush).
Asking for something as simple as opening our lips expresses our utter dependence on G-d for everything we do. Meditating on this idea before beginning to pray can help bring a person to feel humble and insignificant. Humility is praised as one of the ideal attitudes to have when approaching G-d and can enable one's prayers to be accepted.
Another idea: As a result of the first sin man dwells in a coarse and unrefined physical body, which is the root of all the negative attributes to be found in him (See Derech Hashem, part 1 section 3, by the Ramchal). When a person stands in the presence of his Maker with all of his shortcomings, he will feel shame and embarrassment to the point where even opening his lips to speak becomes difficult.
Fear of Heaven
Another explanation: Most of the day, we are involved in casual conversation with co-workers, friends and acquaintances. These situations are hardly intimidating. But how would we feel when pleading with a judge, or when being interrogated by an officer or prosecutor. Even asking our boss for what we feel to be a well-deserved raise would intimidate the average person. How much more should the idea of facing the Omnipotent Creator arouse great fear and trepidation within us. By meditating on the fact that we are now standing before G-d, the Creator of Heaven and Earth, great fear and awe will be aroused within us, rendering us unable to speak.
This is why we refer to G-d in the first person, as if we are speaking directly to Him. The term “Adonai” relates to G-d as our Ruler, and that we are His subjects. This idea should further enhance the intensity one should feel when uttering these words. This explains why we ask G-d for help to open our lips.