I recall hearing that the lion symbolically represents Middat haDin, the attribute of divine justice, but I don't know of a source for this idea.
Is there a source which states that the lion is a symbol for divine judgment?
וּלְדָ֣ן אָמַ֔ר דָּ֖ן גּ֣וּר אַרְיֵ֑ה יְזַנֵּ֖ק מִן־הַבָּשָֽׁן׃
And of Dan he said: Dan is a lion’s whelp That leaps forth from Bashan.
Rabbeinu Bachya writes in his commentary to that pasuk:
דן גור אריה. ע"ד הפשט, המשילו בגבורה לגור אריה כאשר הוא מדלג מהר בשן . דן גור אריה, וע"ד הקבלה נקרא דן כנגד מדת הדין, כי כן אמרה רחל עליו (בראשית ל׳:ו׳) דנני אלהים, והמשילו משה בברכתו לגור אריה כנגד מדת הדין של מעלה ששם צורת גור אריה, וזה מבואר.
Dan is a lion cub. According to the plain meaning of the text Moses compares Dan’s bravery and physical strength to that of a lion, describing how he leaps down from the mountain of Bashan.
A kabbalistic approach: the tribe was called Dan, corresponding to the attribute of Justice. When the original Dan was born his step-mother Rachel had said that G’d had judged her (Genesis 30,6). The reason Moses compared the tribe of Dan in his blessing to a lion was that the celestial image of the attribute of Justice is that of a lion cub.