Team Flash says that Lyla has secured Ramsey at A.R.G.U.S; however, since this happens only hours before the Crisis this is not possible. On Arrow, Lyla was taken from Lian Yu into the void until she returns as the Harbinger. There is no way she would have taken Ramsey, or even known about what was happening at A.R.G.U.S, if she had even been able to answer their phone - which seems to be impossible based on the events that take place on Arrow.