There will be no change to the rights and status of EU nationals living in the UK, nor UK nationals living in the EU, while the UK remains in the EU.
Terrorist attacks in Luxembourg can’t be ruled out. See Terrorism
Around 120,000 British nationals visit Luxembourg every year (Source: STATEC (Statistics Office in Luxembourg). Most visits are trouble-free.
All vehicles must have winter tyres when temperatures are zero or below. See Road travel
If you’re abroad and you need emergency help from the UK government, contact the nearest British embassy, consulate or high commission.
Take out comprehensive travel and medical insurance before travelling.
The Overseas Business Risk service offers information and advice for British companies operating overseas on how to manage political, economic, and business security-related risks.
Source Article from https://www.gov.uk/foreign-travel-advice/luxembourg