Lin Gong and Qing sent troops.

The following conclusion: Lin Gong's death was an important reason for the Qing Emperor to send troops to Northern Qi. The Qing Emperor had always wanted to conquer Northern Qi, but he lacked a reason to send troops. Lin Gong's death gave the Qing Emperor an excuse. The Qing Emperor and Chen Pingping echoed each other and said that Lin Gong's death was the work of Dongyi and Northern Qi, thus achieving their goal of sending troops to Northern Qi. Lin Gong's death also caused the Crown Prince's power to weaken and Fan Xian's power to increase. In addition, the Qing Emperor had also given Minister Lin a big gift on the surface to provide a high-sounding reason for his son's death to send troops to Northern Qi. Thus, Lin Gong's death played a necessary role in the Qing army's invasion of Northern Qi.

Lin Gong's death was an important reason for the Qing Emperor to send troops to Northern Qi. The Qing Emperor had always wanted to conquer Northern Qi, but he lacked a reason to send troops. Lin Gong's death gave the Qing Emperor an excuse. The Qing Emperor and Chen Pingping echoed each other and said that Lin Gong's death was the work of Dongyi and Northern Qi, thus achieving their goal of sending troops to Northern Qi. Lin Gong's death also caused the Crown Prince's power to weaken and Fan Xian's power to increase. In addition, the Qing Emperor had also given Minister Lin a big gift on the surface to provide a high-sounding reason for his son's death to send troops to Northern Qi. Thus, Lin Gong's death played an inevitable role in the Qing army's invasion of Northern Qi.

Lin Gong had been sent by the Eldest Princess Li Yunrui to assassinate Fan Xian.

Lin Gong had been sent by the Eldest Princess Li Yunrui to assassinate Fan Xian.

Lin Gong had been sent by the Eldest Princess Li Yunrui to assassinate Fan Xian.

Lin Gong's assassination of Fan Xian was ordered by the Eldest Princess, Li Yunrui. Lin Gong was Lin Wan 'er's older brother, and also the Crown Prince and Eldest Princess's man. Fan Xian had come to the capital to rob the Eldest Princess of her palace treasury and marry Lin Wan 'er. This had aroused Lin Gong's anger, so he had arranged for Cheng Jushu to assassinate Fan Xian on Niulan Street. Thus, the Eldest Princess had sent Lin Gong to kill Fan Xian.

Lin Gong's assassination of Fan Xian was ordered by the Eldest Princess, Li Yunrui. The Eldest Princess did not want Fan Xian to take over the power of the palace treasury because Fan Xian's enemy was the future Emperor, the Crown Prince. In addition, there were also people like Wu Bo 'an and Prime Minister Lin Ruofu who were related to Lin Gong and felt that Fan Xian and Lin Wan' er's marriage posed a threat to their interests. However, the information on who sent Lin Gong to kill Fan Xian was not clearly mentioned in the search results provided. Therefore, based on the information provided, I am unable to determine who sent Lin Gong to kill Fan Xian.

Eldest Princess Li Yunrui sent Lin Gong to kill Fan Xian. The Eldest Princess did not want Fan Xian to take over the palace treasury's financial power. She also believed that Fan Xian was an enemy of the future Emperor and Crown Prince. Lin Gong was the Eldest Princess's man. He had been sent to assassinate Fan Xian.

Lin Gong's assassination of Fan Xian was ordered by the Eldest Princess, Li Yunrui. The Eldest Princess did not want Fan Xian to take over the power of the palace treasury because Fan Xian's enemy was the future Emperor, the Crown Prince. In addition, there were also people like Wu Bo 'an and Prime Minister Lin Ruofu who were related to Lin Gong and felt that Fan Xian and Lin Wan' er's marriage posed a threat to their interests.

The Qing Emperor knew the cause of Lin Gong's death and the murderer. Although Fan Xian had not personally killed Lin Gong, the Qing Emperor knew that Wu Zhu had killed Lin Gong for Fan Xian. The Qing Emperor was wary and afraid of Wu Zhu's actions because he believed that the Barrette in Wu Zhu's hands could pose a threat to him. The Qing Emperor had asked Fan Xian about the circumstances of Lin Gong's death, but he did not pursue the matter. Thus, the Qing Emperor knew the cause of Lin Gong's death and the murderer.