I think Lilico's approach is more complicated than "it will all be over in a fortnight".
His view is that total cases might peak in 2 weeks (say - on Dec 27th), however, most of those infections will be in the younger age groups who are unlikely to be hospitalised.
If these young low risk individuals socialise with older/vulnerable population between Christmas and New Year, this may lead to a massive spike in hospitalisations and deaths in the first half of Jan. By then cases may be on the way down but the pressure on healthcare may become unsustainable.
There may be hope that Omicron may indeed be "milder" but a 30-50% reduction in virulence will not make a big difference. We need to see a much bigger (e.g. 6-fold) drop to materially influence the end outcome. The best cause of action might be to delay multi-generational gatherings until we have passed the eye of the storm. Lilico suggested that the government gives everyone an extra holiday on January 6 and recommends postponing Christmas celebrations until then.
It is only one person's view but most of his modelling has so far been more accurate than SPI-M projections.