Gemini lagna natives with Venus placed in their 2nd house can expect some positive results in terms of their finances as the 2nd house is related to wealth, possessions and speech among other things. Venus, as the lord of the 5th and 12th houses, will take care of matters related to children, creativity, spirituality, loss and expenses respectively.
The placement of Venus in a neutral sign state indicates that its functioning won't be affected much by its placement. However, it's important to note that even a neutral planet has the power to give results based on how it's positioned in a particular horoscope.
Since Venus is also natural karaka of the 7th house, which relates to partnerships and marriage, individuals with this placement may experience harmonious romantic relationships/partnerships. They may also have good overall social skills and be charming personalities who know how to say the right things at the right time.
Venus' aspect on the 8th house denotes that there could be some unexpected gains or inheritance from unexpected sources. This placement can also indicate a strong desire for intimacy and physical pleasures which may lead them towards indulgence in these areas.
People with Gemini Lagna tend to have an analytical mind and a natural curiosity about life. The presence of Venus in their 2nd house can make them recognize beauty in what they value while adding extra charm to all forms of communication including writing, public speaking or any other form of artistic expression.
Strong financial prospects are indicated by this position due to Venus's role as ruler over Taurus (indicates savings) and Libra (indicates investment). As such investing carefully into equity markets or real estate investments might prove highly lucrative for these individuals.
Individuals with this combination are often very generous souls who can be counted on when it comes time for charitable works\*. Their compassion towards others tends to mean they will go out of their way if someone is in need.
In terms of profession or career, with Venus ruling over the 5th house, it is possible that individuals might be creatively inclined and possess natural artistic talents which may need to be honed and cultivated appropriately. Additionally, as Venus is also the natural ruler of relationships, this placement could give success in careers related to public relations or diplomacy.
Overall people with Gemini lagna and Venus in their 2nd house are likely to be good communicators and often have a charming personality. They tend to be pleasant conversationalists who enjoy entertaining family and friends. With financial prosperity on the horizon, self-care should always remain a priority as there may be a tendency towards indulgence leading them into overspending without adequate planning in place.
It's important to remember that despite predictions based on astrological positions, free will still plays an important part in shaping one's own personal destiny. These brought up astrological aspects should therefore not be considered gospel truth but rather just possibilities that can occur based on astral positions at any given point of time.
\*Charitable works is just a suggestion based on general traits associated with Jupiter significations like Charity & Compassion however giving back to society depends upon one's personal behaviour and belief systems more than anything else so this aspect may or may not hold true for individual cases depending upon their individual beliefs and social conditions they come from.