A late Alan Lithgow header earned Livingston a share of the spoils as they held 10-man Inverness to a 1-1 draw.The hosts broke the deadlock after just six minutes when Aaron Doran curled a low strike into the back of Neil Alexander's net from the edge of the area.Inverness came close to increasing their lead in the 28th minute when Doran's ball in from the right flank hit the bar.Caley Thistle were reduced to 10 men two minutes before the break when midfielder Iain Vigurs was shown a second yellow card.The home side remained an attacking threat in the second half, with Brad McKay and Nathan Austin forcing good saves from Alexander.However, they failed to keep Livingston out at the other end as Lithgow headed the visitors level in the 82nd minute.