Does "check for your watch, Gustaf, he might have lifted it" mean...?

Geeze, it's just lame television humor. He is telling Gustaf (the kind of Sweden is Carl XVI Gustaf) to be careful because Permutter steals things. Yes, one of the meanings of lift is to steal.

Thanks.
Is Carl XVI Gustaf read as Carl the sixteenth Gustaf?

Yes, although in English, we usually call Swedish kings named Carl, Charles. We would say Charles the sixteenth Gustaf.

This practice of anglicising given names is lessening to a certain extent in British usage. For example the Daily Telegraph said in 2010: "Revelations last week that the King of Sweden once enjoyed romps in seedy nightclubs owned by shadowy underworld figures have eclipsed the sparkle of July's wedding. King Carl XVI Gustaf, the stern-looking, bespectacled monarch who is honorary chairman of the World Scout Foundation, has found himself thrust uncomfortably in the spotlight following the publication of an unflinching book, Carl XVI Gustaf – Den motvillige monarken (Carl XVI Gustaf – The reluctant monarch) which catalogues his past predilection for wild, alcohol-fuelled orgies and naked jacuzzi parties with models. "

In the past, the names of people from other language areas were anglicised to a higher extent than today. For royalty, the anglicisation of personal names was a general phenomenon, especially until recently: Charles for Carlos, Karoly, and Karl; Frederic for Friedrich or Fredrik, etc. Anglicisation is still the rule for popes, including recent ones: Pope John Paul II instead of Ioannes Paulus II, Pope Benedict XVI instead of Benedictus XVI.

I have noticed that the Spanish media usually call Queen Elizabeth II "Isabel II" and her name is often spelled with an 's' replacing the 'z' in French and German.

Many military historians, or amateur fans of history (the bane of serious historians) would immediately know who you were talking about if you said Charles XII, one of the most overrated military leaders in history. If you wrote Carl XII, they'd probably have no clue.