From Longman Dictionary of Contemporary Englishlook up phrasal verb1 IMPROVEif a situation is looking up, it is improving SYN improve, get better Now the summer’s here things are looking up!2 FIND OUT look something ↔ up if you look up information in a book, on a computer etc, you try to find it there Look the word up in your dictionary. I’ll just look up the train times.3 VISIT look somebody ↔ up to visit someone you know, especially when you are in the place where they live for a different reason Don’t forget to look me up when you come to Atlanta. → look→ See Verb table
Examples from the Corpus
look up• There was a loud bang outside the classroom, and we all looked up.• I looked up a few old friends while I was in Birmingham.• "Goodbye, then, " she said, without even looking up from her book.• If you don't know what it means, look it up in the dictionary.• If you look up the title of the book, you should then find the author.• I'll give you my address so you can look me up whenever you're in London.things are looking up• However, following the campaign of certain organisations and individuals like Jaqueline Drake, things are looking up.• Some industry analysts are convinced that things are looking up for the business.• Things are looking up - I've got a new job and a new boyfriend.• As we said, things are looking up in these parts.From Longman Business Dictionarylook up phrasal verb [intransitive] if a situation is looking up, it is improvingThings are looking up for High Street retailers. → look→ See Verb table 