Venus is one of the most auspicious and beneficial planets in Vedic astrology. It represents love, beauty, marriage, relationships, luxury, comforts, wealth and prosperity. However, when Venus is placed in the 3rd house for Sagittarius lagna, it is in an enemy sign state.
The placement of Venus in the 3rd house can result in some challenges for Sagittarius natives. The third house represents communication, courage, confidence and siblings. Therefore, this placement suggests that communication with others could be a challenge for Sagittarius natives. They may struggle to express themselves clearly or articulate their thoughts and feelings effectively.
However, despite being in an enemy sign state, Venus takes care of its own houses - the 6th and 11th houses - as it is their lord. Thus, this placement can also lead to positive results related to these houses. The 6th house represents enemies, obstacles and diseases while the 11th house represents gains and networking abilities.
Sagittarius natives with this placement of Venus may find that they are able to overcome enemies and obstacles successfully in life due to Venus' influence on the 6th house. They may also benefit from networking skills gained through Venus' influence on the 11th house.
Venus is also a natural karaka or significator of relationships represented by the 7th house. This means that even though Venus is not directly located in the seventh house but influences positively because it's Karaka planet for relations for Sagittarius ascendant born people.
On another note since it aspects (looks) on to the following houses [9] which represent fortune/luck/knowledge etc., some astrologers suggest that this placement has the potential to bring good luck or financial gains through knowledge-based pursuits such as education or spiritual practices.
Venus' aspect on ninthhouse can make Sagittarius lagna natives more prone towards spiritual inclination in life, travel overseas or could inherently possess intellectual personality traits. Since Venus is a planet of luxury and wealth, these gains may lead to an increase in material comforts and pleasures.
In conclusion, Sagittarius natives with Venus placed in the 3rd house should expect challenges related to communication but can also benefit from Venus' influence on their 6th and 11th houses which could lead to triumph over their enemies as well as networking benefits. They may also experience good luck and financial gains through knowledge-based pursuits due to Venus' aspect on the ninth house. It's safe to say that there are always mitigating factors based on placement of other planets such as conjunctions or aspects affecting this placement of Venus for Sagittarius Lagna born people-- hence it is always better consult an experienced astrologer for personalized interpretations of one's chart.