The NET translates this passage thusly
But Moses replied to the Lord, “If the Israelites did not listen to me, then how will Pharaoh listen to me, since I speak with difficulty?”
Their justification for this is helpful and can be found in the notes provided along with the translation
The “lips” represent his speech (metonymy of cause). The term “uncircumcised” makes a comparison between his speech and that which Israel perceived as unacceptable, unprepared, foreign, and of no use to God. The heart is described this way when it is impervious to good impressions (Lev 26:41; Jer 9:26) and the ear when it hears imperfectly (Jer 6:10). Moses has here returned to his earlier claim – he does not speak well enough to be doing this.
The first step in the conversion process to Judaism (for men) was circumcision.(Genesis 34) Babies born into Judaism were to be circumcised on the 8th day and slaves which were purchased were to be immediately circumcised and this was to be a sign of God's covenant with His people. (Genesis 17)
Therefore, any who were uncircumcised were not dedicated to the LORD and unfit for His service. For this reason, anyone wishing to participate in Passover had to be circumcised.
Similarly, Moses had to be circumcised before he was fit for service to the LORD and he was not allowed to go before Pharaoh before he was circumcised. This was therefore Moses' way of saying that he was unfit for service as the mouthpiece of Israel.
Another interesting aspect of this is that there are many scholars who believe Moses may have had a speech impediment - a tradition which has been around for quite some. In antiquity, the culture was extremely superstitious. Any malady, infirmaty, handicap or disorder was typically thought to be a result of sin - even accidents and so forth. It is for this reason that we see this passage in John 9:1-2
Now as Jesus was passing by, he saw a man who had been blind from birth. His disciples asked him, “Rabbi, who committed the sin that caused him to be born blind, this man or his parents?”
Furthermore, being unclean was synonymous with being sinful. This is why there was often little separation between being unclean due to something like Leprosy and being unclean due to a sinful deed. Unfortunate afflictions like Leprosy were simply proof of one's sinful deed. If Moses' mouth was unclean due to a speech impediment or oral deformity, saying he was uncircumcised is another way to say that his mouth is unclean.
This can be seen in Leviticus 12:1-3 in which a woman becomes clean again after 7 days by circumcising her Son. For this reason, those who were uncircumcised were also unclean. (Isaiah 52:1)
Wake up! Wake up! Clothe yourself with strength, O Zion! Put on your beautiful clothes, O Jerusalem, holy city! For uncircumcised and unclean pagans will no longer invade you.
Moses' lips were uncircumcised because Moses thought they were unfit for service to God. They were uncircumcised because they were unclean due to sin which can be seen and heard in his speech deformity. For this reason, Moses' speech was described as "faltering" and "unskilled" and Moses was said to speak "with difficulty" in other translations. Moses believed his lips were sinful, unclean and generally unfit for service to God as a result of his trouble with speech and thus describe his lips as "uncircumcised".