There is no direct public transportation leaving from Lalibela to Mekele. What one can do is, drive 180 k/m from Lalibela -Woldia, there switch a mini-van or other cars driving direct to Mekele.
Highland Eco Trekking Tours also offer a private car rental to Mekele and all destinations in Ethiopia.
You get a free drive from Lalibela to Mekele, If you book your Danakil Danakil Depression tour with Highland Eco Trekking Tours Ethiopia
Recently Ethiopian Airline has started 3 weekly flights from Mekele to Lalibela.