Is it licit to pray Lauds at any time in the morning?
Yes it is.
Many times I pray it at 3am.
I like to pray Lauds at sunrise but there are times I pray it after 7. Although I will not pray it after 8am since it’s so close to Terce.
Decades ago, with the 3-nocturn matins to start the office with obstructing lauds it was very hard to pray the hours at the proper times - a priest friend of mine told me he left the entire office for the night as he didn’t have time earlier - with the advent of Vatican II and the LOTH it’s practically a lack of proper care not to pray the hours at the right time. I get up at 7 and immediately pray lauds and then the unbelievably shortened Office of the Readings (the former matins) - As prime has dissappeared and only one little hour is required I pray Sext before lunch - At sundown I pray vespers and in my bed around 11 pm I pray compline by heart (you can use every day the Saturday or Sunday complines) - I have all time used the Latin Pian Psalter (Pius XII’s) which is more practical and understandable.