If there was an anti-Lloyd George candidate for the leadership in the Liberal party, it would most likely have been Sir John Simon. Until he resigned as Home Secretary in January 1916 because of his opposition to conscription he was regarded by many as Asquith's most likely successor.
Simon would have got the support of the pacifist and anti-conscriptionist wing of the party and those who were Asquithians in OTL. But LG would have become Liberal leader and Prime Minister. The two men at best barely tolerated each other.
The coupon election of December 1918 happens as in OTL, and Simon loses his seat in Walthamstow. Sometime in 1919 or 1920 he returns to the House of Commons in a by-election caused by the resignation or death of a sitting Liberal MP.
The LG headed coalition falls in October 1922 as in OTL. The general election on 15 November 1922 is won by the Conservatives under Bonar Law. The Liberals are divided between National Liberals under LG and Independent Liberals under Simon.
Events proceed as in OTL: Bonar Law resigns because of ill-health, Baldwin becomes Prime Minister and calls a general election on the issue of protection. The Liberals are re-united under Simon. The result of this election on 6 December 1923 is similar to that in OTL: the Conservatives are the largest party in the House of Commons, but can be outvoted by Labour and Liberals combined. In the critical vote which brought down Baldwin's government on 21 January 1924 only ten Liberals voted with the government, all of them former Coalition or National Liberals.
At a meeting of the Liberal shadow cabinet on 27 May 1924, LG and Simon were among those who urged that they should vote with the Conservatives on the failure of the Labour government to reduce unemployment.
But Asquith was still willing to postpone a crisis which might jeopardise his and the party's survival, and he evaded his colleagues' pressure by deciding to put the matter to a party meeting. Here the feeling was much less bellicose. The "general opinion", "frankly expressed", was that it was not in the Liberals' interest to precipitate an election
The decision of the party was to vote with the government. (1)
If Simon had been Liberal leader and the party had voted with the Conservatives, the government would have been defeated and there would have been a general election in late June or early July 1924.
The Red Scare issues of the Russian loan and the Campbell Case would not have featured in the election, though I don't know about the Zinoviev letter. Therefore the Conservatives would have not done as well as they did in October 1924 general election in OTL when they won 419 seats, but I expect would win an overall majority.
In this scenario Simon stays on as Liberal leader. But in OTL although a member of the committee set up by LG in 1927 which investigated British industry, "he played little part in its deliberations, and only at the last moment agreed to sign its report." (1)
So the Liberal party programme in a 1928 or 1929 general election fought under Simon's leadership would have been less radical than that under LG in 1929 in OTL.
If such a general election resulted in Labour becoming the largest party but without an overall majority, the Liberals would have been divided on whether to keep the Tories in or put Labour in. In OTL in the May 1929 general election, the Tories did not contest Simon's constituency of Spen Valley (one of only 25 seats which they did not contest), so presumably they thought he was close enough to their views.
If the Liberals voted to keep the Tories in, I expect the radical wing under LG would have broken away. With a more right-wing Liberal Party the Liberal Nationals in OTL would probably have stayed Liberal. Simon was born in 1873 so he was not too old to continue as Liberal leader during the 1930s.
(1) Taken from
The Downfall of the Liberal Party 1914-1935 by Trevor Wilson.