The night following (tēi epiousēi nukti). Locative case, on the next (following) night.
The Lord (ho kurios). Jesus. Paul never needed Jesus more than now. On a previous occasion the whole church prayed for Peter’s release (Act 12:5), but Paul clearly had no such grip on the church as that, though he had been kindly welcomed (Act 21:18). In every crisis Jesus appears to him (cf. Act 18:9). It looked dark for Paul till Jesus spoke. Once before in Jerusalem Jesus spoke words of cheer (Act 22:18). Then he was told to leave Jerusalem. Now he is to have “cheer” or “courage” (tharsei). Jesus used this very word to others (Mat 9:2, Mat 9:22; Mar 10:49). It is a brave word.
Thou hast testified (diemarturō). First aorist middle indicative second person singular of diamarturomai, strong word (See note on Act 22:18).
Must thou (se dei). That is the needed word and on this Paul leans. His hopes (Act 19:21) of going to Rome will not be in vain. He can bide Christ’s time now. And Jesus has approved his witness in Jerusalem.