The strike, over pay and working conditions, is likely to cause the cancellation of hundreds of flights.
It will affect Lufthansa passenger services at all airports in Germany, as well as Lufthansa Cargo and low-cost carrier Germanwings.
If it goes ahead, it will be the third strike to hit Frankfurt airport, Lufthansa's home base, in six weeks.
The airline's management is urging the pilots' union, Vereinigung Cockpit (VC), to come back to the negotiating table as soon as possible.
"With the good will of everyone involved, we should be able to avert a strike," said Lufthansa's head of personnel, Dr Bettina Volkens.
In the meantime, the airline says it will take whatever steps it can to minimise the effect of a strike on its customers.
But it said: "We regret very much that from April 2 to April 4 we probably won't be able to get our passengers to their destinations or home as planned".
Pilots at Lufthansa will hold a three-day strike from 2200 GMT on 1 April, their union has announced.