Let's begin with the absolutely most superficial and work our way in, shall we? Haman and Lacus both have "warm" hair colors, specifically Lacus has pink, and Haman a more magenta shade. Obviously they're not that far apart. Both are young, beautiful, blue eyed women. Both are space-born women of a race despised by the people of Earth. Both have a tendency to accentuate their hair with golden ornaments.
At a young age, Haman Khan was rescued from peril by a dashing young prince. Lacus, likewise, was rescued from mortal peril by one she later referred to as a knight, whose sister was a princess. Haman was a sweet teenager, and continued this public appearance of being a perfect lady the rest of her life. An act Lacus endeavored to put on as well. Haman became romantically interested in Char Aznable when she was young, just as Lacus was engaged to Athrun Zala, one of SEED's three Char Clones at a young age. Despite this relationship, both Haman and Lacus later moved on from their Char to a bright eyed young man with big dreams about an idealistic version of the universe.
The Haman Khan we know, particularly in ZZ, has a tendency to use her femininity to influence the men in her life into doing her bidding. She does this with Glemy, with Mashmyre, and even Judau. This is symbolized differently with all three, but most blatantly with Mashmyre's rose. Lacus also uses her femininity to influence the men in her life, collecting Kira, Athrun, and Andrew Waltfeld to her cause as time goes on.
Haman's father was a prominent member of Spacenoid society, and when he died, she took over his role in Axis society. Lacus' father was a prominent member of Coordinator society, and when he died she claimed his role in the PLANTs.
Both women are charismatic, but extremely talented tacticians and cunning manipulators of the persons and events around them. Haman was also a NewType, and Lacus a SEED bearer. Haman suggests that concealing her true nature is her greatest strength, and as previously discussed, disguising the fact that she (Lacus) is so intelligent is likely Lacus' as well. Haman tells Judau that it is the destiny of humans to be alone. Lacus fights Durandal's communal "Destiny Plan" leaving humans alone to find their own way through life.
Both women are intensely ambitious, Haman ruthlessly fighting to seize control of the Earth Sphere and Lacus raising a small army of her own for the sake of dictating human fate as well.
For the sake of reminder, consider: Lacus Clyne orchestrates the induction of Kira Yamato into her personal command, the theft of the newest and most powerful Gundam for this same sake, and a new ship prior to entering into a two-way conflict, where, in spite of being a relative unknown, she quickly gains power and sway over all after a conflict with Athrun Zala. Some time later, her forces engage a distressed and disorganized world in a conflict for control of the fate of mankind.
Haman Khan attempts the induction of Judau Ashta into her personal command, as well as the theft of his newest and most powerful Gundam for the same sake, and the new prototype ship. She enters into a two-way conflict between the Titans and AEUG where, in spite of being a relative unknown, she quickly gains power and sway over all after a conflict with Char Aznable. Some time later, her forces engage a distressed and disorganized Earth Sphere in a conflict for control of the fate of mankind.
Lacus is friends with an actual princess that everyone knows is a puppet and ignores in her favor. Haman is the guardian of an actual princess that everyone knows is a puppet and ignores in her favor.
