Could he stay opposed to conscription and challenge Asquith for primacy from within the main of the Liberal party? Challenge Asquith on basis of fitness to lead and suitability for power compared to an older, ill opponent?
Actually, it was necessary to introduce conscription, but IOTL DLG even went further by demand conscription of married men, which was (somewhat correctly) opposed by McKenna and Keynes on the ground that this would eventually lead to bankruptcy.
In post 4, there was a timeline in which DLG used Temperance Movement to oust Asquith in a more legitimate way.
Or just simple, Lloyd George allow Asquith to be in the War Committee as a nominal member. IOTL he excluded Asquith while included Edward Carson (this was a true humiliation towards Asquith), causing him to resign (actually, this was also Asquith's mistake as he falsely believed that DLG could never form a government). If he decided not to include Carson, Asquith might swallow his pride and accept to be a figurehead PM, but this would have reduced Asquith to a figurehead--that the only control the Prime Minister and his Cabinet had over the War Commission was a veto that they would not dare to use for fear of bringing on themselves the collective resignation of the War Commission. Nevertheless, with the Leader of the Liberal Party still being Prime Minister, even in a weakened position, this could prevent the split. At least prior to December 1916 Liberals might have hoped that an improvement in the war situation might rescue them from disaster.
Have Asquith accept to serve under DLG as Lord Chancellor right after the coup would help maintain the balance in the Coalition, but this seems unthinkable after a too blatant back-stab (from Asquith's view).
The final chance I think would be the months before the 1918 Coupon election. DLG said in 12th November that: "Revolution I am not afraid of. Bolshevism I am not afraid of. It is reaction that I am afraid of". This was praised by Asquith and Wilson, who advocated a clean peace. However, he decided to accept the limit on Coalition Liberal MPs and join Bonar Law, and during the election he did exactly the opposite, with things like "hanging the Kaiser", partly due to the fact that he had to act in line with the Tories. Worse, he denounced Labour as Bolshevik and even lambasted his own party.
There is also no doubt that whether or not Lloyd George had conspired to bring about Asquith's downfall, a great many people *assumed* he had done so, and this not only helped to keep the Liberal Party divided, but also added to Lloyd George's reputation for unscrupulousness--which is one reason why, when the Conservatives abandoned their Coalition with him a few years later, it was difficult to find much sympathy for him or any sense that *he* had been betrayed. As a popular rhyme put it:
Lloyd George, no doubt,
When his life ebbs out,
Will ride in a flaming chariot,
Seated in state
On a red-hot plate
'twixt Satan and Judas Iscariot;
Ananias that day
To the Devil will say,
"My claim for precedence fails,
So move me up higher,
Away from the fire,
And make way for that liar--from Wales!"
Even when he became official party leader later IOTL, many hated him and opposed him, notably Runciman. During 1929 election, Labour found no difficulty to attack him due to his unscrupulousness and his ìnfamous Homes fit for Heroes.