The row comes at an embarrassing time for Mr Lawrence, who last week castigated the Treasury for failing to disclose sensitive information at the time of the pounds 4bn sale of shares in the electricity generators in March.
Stock Exchange users, who contribute to the institution's revenue, want to know how Mr Lawrence's bonus payments are calculated and who the members of the committee were who took the decision to award them.
A draft copy of the Stock Exchange annual report shows that the exchange intends to pay Mr Lawrence a pounds 100,000 bonus, which takes the overall remuneration package for his first year in the job to about pounds 422,000.
The draft report also shows that the exchange intends to pay Giles Vardey, markets developments directior, a pounds 75,000 bonus, taking his overall package to around pounds 230,000.
The row is expected to escalate in the next fortnight, with the publication of the final version of the annual report, although the figures for the executives' remuneration packages could be subject to change.
News of the exchange's intentions caused a stir at a conference of about 300 private-client stockbrokers held in Glasgow two weeks ago. One of those present, Keith Loudon, a senior partner at Redmayne Bentley, private client stockbrokers, said last week: "If the exchange's bonus payments were as reported in the draft of the annual report, the stockbroking industry will want to know who set the targets that had to be achieved to receive such payments and what those targets were."
Mr Loudon was critical of John Kemp-Welch, the exchange's chairman, at the meeting for not answering questions from the floor after the chairman's speech about the future of the exchange.
The Independent has been told that the Stock Exchange board was informed last November that the remuneration committee had "received the objectives of the chief executive and the members of the executive committee". However, the board was not told at that time what these objectives were.
The Stock Exchange declined to say whether its board members had since been informed of the senior executives' targets, although one source said that it would not be usual for the board to know of these targets. They would know about them, however, in the event of an individual not achieving them.
Members of the remuneration committee, one source said, include Donald Brydon, deputy chief executive of BZW, John Bond, group chief executive of HSBC Holdings; Michael Marks, chairman of Smith New Court; Miles Rivett- Carnac, Barings; and Nick Verey (Warburg Securities).
Friends of Mr Lawrence have said that his first full year at the exchange has witnessed a number of successes: the exchange has moved successfully to a new rolling settlement system for share transactions and AIM, the new market for small companies, is due to open next week.