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All English, as you thought.
Lazenby - a Yorkshire name in my opinion. There are two places in the old North Riding of Yorkshire with this name; one near Middlesborough, the other near Northallerton. The name is Old Norse Leising+by, "freeman's farm". The earliest notices of the surname that I've seen are of a family residing at Lazenby near Middlesborough.
There is also a Lazonby in Cumbria, same meaning, but I stick to the Yorkshire provenance.
Comely - looks like it's the comely meaning "attrctive, handsome", but Basil Cotton ("Penguin Dictionary of Surnames")suggests a possible place name origin, e.g., Combley in the Isle of Wight, meaning "clearing in a combe" or valley.
Casely - a version of Kearsley, according to Reaney and Wilson. There are sevaral Kearsleys in England. The one in the Greater Manchester area means "clearing where cress grows". The others (Northumberland, Warwickshire) probably have tha same meaning.