LIZA MINNELLI is so distraught over her sister’s cancer battle that friends fear she’ll relapse into boozing and pill-popping!

The “Cabaret” star began a downward spi­ral after her half sister, Lorna Luft, 60, announced that she was recovering from breast cancer surgery and undergoing chemotherapy, sources say.

“Liza was absolutely devastated when she first got the news Lorna had breast cancer,” said a source close to the 67-year-old Oscar winner.

“IT HIT HER HARD, AND SHE STARTED WORRYING about her own mortality!

“The fear is that Liza will start hitting the bottle.”

The talented entertainer has bounced in and out of rehab since the mid-’80s for addictions to booze and drugs, and she’d fallen off the wagon a few times in the past year, said a friend.

“Liza had been making strides toward staying sober, but Lorna’s cancer operation could undo all that,” said the source.

Liza and Lorna – daughters of famed “Over the Rainbow” singer Judy Garland – became estranged in 1994 when singer Lorna took a tough-love stance over Liza’s substance abuse problems.

Their feud ended in 2005 when Lorna’s 89-year-old father Sid Luft, Garland’s third husband, passed away, and in February, Liza turned out for the debut of her sister’s latest show in New York.

Meanwhile, as The ENQUIRER recently re­ported, pals have become concerned the “New York, New York” star is suffering from early-onset dementia.

The source added: “For Liza, Lorna’s cancer could be the straw that breaks the camel’s back – and could have her turning to booze and drugs to ease the pain!”