From Longman Dictionary of Contemporary Englishfit somebody/something ↔ out phrasal verb British EnglishPUTto provide a person or place with the equipment, furniture, or clothes that they need The office had been fitted out in style. with The new recruits were fitted out with uniforms and weapons. → fit→ See Verb table
Examples from the Corpus
fit out• The slow and laborious nature of the work has meant that the fit - out has taken considerably longer than anticipated.• This check up shows he's fully fit to carry out his strenuous lifestyle as a hospital porter.• He fitted her out with catalogues galore.fit with• He fitted her out with catalogues galore.From Longman Business Dictionaryfit something → out phrasal verb [transitive] to provide a room, building etc with decorations or equipment withThese boats are usually fitted out with electronic gear that costs thousands of dollars. → fit→ See Verb table 