* Richemont hits record high

* Lufthansa slides as Thiel family halves stake

* Euro zone business growth hits three-year high

May 21 (Reuters) - European stocks rose on Friday, as Swiss luxury goods maker Richemont jumped after its results and accelerating business growth in the euro zone kept investors cautiously optimistic in the face of rising inflation worries.

The pan-European STOXX 600 index rose 0.6%, capping the week with a small gain.

Cartier-owner Richemont rose 5.0% to a record high as it proposed doubling its dividend back to pre-pandemic levels after strong demand for jewellery helped lift net profit and contain the fall in sales in its fiscal year 2020/21.

IHS Markit's survey showed euro zone business growth accelerated at its fastest pace in over three years in May, helped by a strong resurgence in the bloc's dominant service industry as economies reopened.

A gauge of British economic growth hit its highest level on record in May as many services firms reopened their doors and factories rode a wave of demand from a recovering global economy, prompting a jump in both hiring and prices.

"The picture today for risk assets looks a lot more positive than it did mid-week... and today's suite of stronger economic data provides a continued argument to stick with equities," said Chris Beauchamp, chief market analyst at IG.

"However, until we clear the peaks seen a week ago some caution will linger."

Global equities have struggled to make headway after hitting record highs earlier this month, as investors fear that higher inflation could prompt central banks to pare back pandemic-era support more quickly than expected.

However, European Central Bank President Christine Lagarde said it is still too early for the central bank to discuss winding down its 1.85 trillion euro ($2.25 trillion) emergency bond purchase scheme, less than two weeks ahead of a crucial policy meeting.

German luxury carmaker BMW rose 0.7% after it said it would have to set aside 1 billion euros, less than initially feared, for expected European antitrust fines for alleged collusion with rivals.

Lufthansa AG fell 6.5% as the Thiele family, the second-largest shareholder in the German airline, sold more than half of its stake.

Italian banks were mixed, with Bper Banca and Banco BPM inching up, while Unicredit and Banca Monte dei Paschi di Siena slipped after a report that Italy was discussing with the European Union new rules that would ease deals between more than two banks.

Unicredit also said it contested a decision by EU antitrust regulators to fine the Italian bank and others 371 million euros for taking part in a European government bonds trading cartel. ($1 = 0.8213 euros) (Reporting by Sruthi Shankar and Shreyashi Sanyal in Bengaluru; Editing by Arun Koyyur and Susan Fenton)