Problem One: Lyons was a lifelong pacifist who at the time of his death was sinking into deep depression at the prospect of a new Great War.
Problem Two: Robert Menzies still has a lean and hungry look
Problem Three: Labor won't join a wartime National Unity Government as John Curtin knows that to do would split the ALP and Lyons is also viewed as a "rat" and a traitor by Labor.
Problem Four: the OTL 1940 federal election was a hung parliament for the UAP-Country government and that was with a new PM would had only been in office a year. With Lyons, who has been PM since 1932, the UAP-Country government might lose outright. An earlier Curtin government causes many butterflies to start flapping.