Sun represents the soul and vitality of a person, whereas the first house represents the self or persona of an individual. The placement of Sun in the 1st house for Gemini ascendant gives rise to some interesting astrological predictions. In this position, Sun is exalted as it is in its friend sign state which indicates that it will work harmoniously with the energies of Gemini lagna.
The lordship of Sun over the third house signifies that it takes care of communication, relationships with siblings, courage and efforts put into workplace. This means that individuals with Sun in their first house can be confident communicators and may enjoy good relations with their siblings. They may also have considerable courage and determination in their professional lives.
Moving on to natural significations based on Sun's karaka houses i.e. 1st and 10th houses, we see that this placement must have powerful effects on career matters, standing in society etc. Since sun is placed in a good House (1st) for these key areas an individual can expect fame and recognition from others based on their unique talents or personal endeavors. Such are usually admired by others for being creative, courageous and innovative.
On examining Sun's aspect on the seventh house - which governs partnerships - it appears this could bring about positive impact on relationships whether personal or professional as well by making a person focused & confident while initiating new partnerships be it romantic or business/gaps fillers where one partner covers other deficits.! This aspect could also make them loyal partners well-matched with someone who prefers them to be transparent about everything from communication to partnership benefits making allies cherishing honesty than deception at any point!
Overall, it looks like a very positive period for people born under Gemini Lagna. With Sun's energy being combined with Mercury's (ruler of Gemini), individuals get an added dose of charm & wit to compliment all aspects mentioned earlier.The energies working together encourage higher cognitive abilities, intellectualism, optimism and adventurousness!
It would be interesting to note that while Sun is exalted in first house for Gemini Ascendants, this same position can lead to arrogance or overconfidence which could work against long-term goals. Such a scenario will require timely corrective measures if they want to maintain their success rate hence it's very important not to confuse self-confidence with arrogance.
In conclusion, Sun's placement in the first house can definitely bring about positive change for individuals born under Gemini Lagna by boosting abilities related to personal identity & influence as well as strong bonding capabilities (whether with siblings or partners). It appears likely that these people may find themselves enjoying professional development alongside love life at this stage of life. However, given due cautions are taken necessary adjustments made one can make the most astrology's gifts within reason.Such balanced attention will surely help them boost confidence when working on personal strengths areas without stepping on other parts of human lives that also need support.