They made their demand in the Seoul High Court which is hearing an appeal by Lee against a five-year jail term handed out to him in August by a lower court in the case that has gripped the country.
The 49-year-old billionaire heir to South Korea's Samsung Group was convicted by the lower court of bribing the country's former president Park Geun-hye. Besides Lee, who has been in detention since February, four former Samsung executives were also charged in the case.
The lower court had ruled the bribe helped Lee strengthen his control of Samsung Electronics, the crown jewel in the country's biggest conglomerate and one of the world's top technology firms.
"The defendants say they are concerned about the future of Samsung Group. However, what they are really concerned about is Lee's loss of control and subsequent economic losses," special prosecutor Park Young-soo told a packed court of about 150 people.
Lee, in a dark suit and white shirt without a tie at the appeals hearing, earlier on Wednesday denied the bribery charge and also denied recent allegations by prosecutors that he had met Park one-on-one four times, instead of the previously disclosed three times.
The Seoul High Court is expected to rule on the appeal in late January. Whichever side loses could take the case to the Supreme Court, the final court of appeal in South Korea.
The lower court had ruled in August that while Lee never asked for Park's help directly, the fact that a 2015 merger of two Samsung affiliates did help cement Lee's control over Samsung Electronics implied he was asking for the president's help to strengthen his control of the firm.
His lawyers have strongly challenged this logic since appeals hearings began in October.
"The defendants have not once tried to solve issues by colluding with political power and gaining its help. The special prosecution has severely distorted the truth, and that distortion is reflected in the jail term they sought," said Lee In-jae, Lee's lawyer, responding to the 12-year jail term demand.
The scandal played a big part in the downfall of former president Park, who was dismissed in March after being impeached, and the case cast a critical eye over the ties between South Korea's chaebols - big family-owned corporate groups - and its political leaders.
Faced with investor worries of a leadership vacuum as Lee remains detained, Samsung Electronics appointed a new generation of top managers at its three main businesses including semiconductors in October.
Lee has been widely expected to follow in his father, Lee Kun-hee's, footsteps in the future. Lee Kun-hee, the chairman of the group, has been hospitalized since 2014.
Answering a prosecutor's question about his future as Samsung heir, Lee said: "I had been privately thinking that Chairman Lee Kun-hee will be the final person to have the title of Samsung Group chairman."
"I have often said that I want to be a businessman who is recognized for capability, not just for being someone's son, or for having a lot of shares."
(Reporting by Joyce Lee; Editing by Himani Sarkar and Muralikumar Anantharaman)
By Joyce Lee