Energy, mining stocks boost Australia shares to 4-month high

* Benchmark records best session in 15 months

* Energy, travel stocks rise on demand optimism

* Lynas Rare Earths hits decade-high

* Coal exporters gain on Indonesia export ban

Jan 4 (Reuters) - Australia shares jumped 2% on the first trading day of the year on Tuesday, notching their best intraday session in 15 months, as a surge in commodity prices lifted heavyweight energy and mining sectors.

The S&P/ASX 200 index closed higher at 7,589.8 on Tuesday, their strongest closing level since mid-August. The benchmark climbed 13% in 2021.

Investors appeared to show scant response to reports of local COVID-19 infections hitting a record high and hospitalisations rising due to the Omicron coronavirus variant, with the Australian government remaining headstrong in its decision to reopen the economy.

Mining stocks, which comprise more than a third of the benchmark, rose 2.2% to hit a four-month high on strong iron ore prices. Shares of BHP Group climbed 2.1% and Fortescue rose 3.3%.

Lynas Rare Earths, the largest rare-earths producer outside China, added 8.5% to hit a near 10-year high after the company got environmental approvals last week to build a permanent disposal facility for water-leached purification residue in Malaysia.

Energy stocks climbed 3.9%, their most in more than three months, as oil prices rose on the prospect of demand recovery for the commodity in the coming year.

Brad Smoling, managing director at Smoling Stockbroking, said demand optimism for travel was behind the rally in energy and travel stocks.

Investment firm Washington H Soul Pattinson and Co and Woodside Petroleum led gains among energy stocks, up 4.7% and 3.4%, respectively.

Coal miners Whitehaven Coal and Yancoal Australia jumped 5.8% and 7.7%, respectively, as prices rose sharply following Indonesia's coal export ban.

Travel management firms Flight Centre Travel, Corporate Travel Management and Webjet clocked gains between 4.2% and 5.7%, while carrier Qantas rose 2.8%.

Markets in New Zealand were closed on Tuesday, and will resume trade on Wednesday, Jan. 5.

(Reporting by Harshita Swaminathan; Editing by Sherry Jacob-Phillips)