Yes, Lufthansa does offer compensation for cancelled flights under certain conditions, especially when the cancellation is within their control. According to EU Regulation EC 261/2004, if your Lufthansa flight is cancelled and you were informed less than 14 days before departure, you may be eligible for financial compensation. The compensation amount typically ranges between €250 and €600, depending on the flight distance and the length of delay experienced due to the cancellation. However, if the cancellation was caused by extraordinary circumstances such as severe weather, political unrest, or air traffic control strikes, Lufthansa may not be obligated to compensate passengers.

In addition to monetary compensation, Lufthansa also offers care and assistance in the event of cancellations. This may include meal vouchers, hotel accommodation, and alternate transportation. If a suitable alternative flight is not provided, passengers are entitled to a full refund of their unused ticket portion. Passengers flying from or to the EU, or on an EU-based airline like Lufthansa, are well-protected under EU aviation law.

To claim compensation, you can contact Lufthansa directly through their customer service or fill out an online compensation claim form on their official website. It is advised to keep all relevant documents including boarding passes, tickets, and any communication from the airline regarding the cancellation. Also, noting the exact time of the notification and the reason for the cancellation can strengthen your claim.

If you're unsure about your eligibility or require help navigating the claims process, you can also reach Lufthansa’s support at +1-(833)-845-1858. Their representatives can assist with flight cancellation policies, rebooking options, and potential compensation queries. Always review the terms and conditions on Lufthansa’s website to stay updated with any policy changes regarding cancellations and compensation.