Alright, research done...
There are fifty-seven Liberal Democrat MP's, and therefore forty-three of them will have to vote in favour of any proposal for it to be agreed. So far, so easy... The apparent mystery is the Federal Executive. So, here is your 'cut-out-and-keep' guide to the Federal Executive...
8.1 There shall be a Federal Executive, which shall be responsible for directing, co-ordinating and implementing the work of the Federal Party. It shall consist of the following:
(a) the President, who shall act as its chair;
(b) the Vice-Presidents;
(c) the Leader;
(d) two other MPs elected by and from the Parliamentary Party in the House of Commons;
(e) one Peer elected by and from the Parliamentary Party in the House of Lords;
(f) one MEP elected by and from the Parliamentary Party in the European Parliament;
(g) two principal local authority councillors elected by principal local authority councillors of the Party from among their own number;
(h) one representative of each State Party, elected by its internal procedures (State Parties may appoint a substitute member should the elected member be unable to attend a specific meeting of the Federal Executive);
(i) one more person than the total number of voting members elected or appointed under paragraphs (a) to (h) above elected by the Federal Conference (casual vacancies shall be filled in accordance with the electoral regulations) except that persons who, at the date of close of nominations for election under this paragraph, are MPs shall not be eligible to be candidates for election under this paragraph.
Filling in the gaps, there are three Vice-Presidents and three State Parties, so that there are fifteen elected under paragraph (i). Therefore, there are twenty-nine members of the Federal Executive, twenty-two of which would need to vote in favour of accepting any proposal.