"The Lamar situation still weighs on her," a sources tells PEOPLE

By Elizabeth Leonard and Lanford Beard
Updated December 22, 2015 02:45 PM
Credit: Gregg DeGuire/WireImage ; Jason LaVeris/FilmMagic

With the holidays underway, Khloé Kardashian continues to support Lamar Odom as his health improves little by little.

PEOPLE has learned that Kardashian, 31, will continue her regular visits with Odom, 36, as he makes slow but steady progress in regaining the cognitive and motor functions he lost when he was hospitalized in October after a near-fatal overdose.

Even as her famous family prepares for its annual Christmas celebrations, a source tells PEOPLE that “the Lamar situation still weighs on Khloé. She’s not one who just walks away.”

The source continues, “She’s going to be there for him, but she also needs to start focusing back on herself – and she knows that.”

Kardashian previously told PEOPLE she was committed to providing unwavering support for the former NBA player, 36.

“There is a very long road ahead of [Lamar],” she said in October. “He has to walk that road by himself, and, most importantly, he has to want to walk that road. I will be there supporting him every step of the way.”

RELATED VIDEO: Khloé Kardashian Wanted Lamar Odom Transferred to L.A. So He Can Get the ‘Best Medical Treatment Possible’ Says Source

And, despite reports this week that Odom is indeed physically walking that road, a source at Cedars-Sinai tells PEOPLE that “Lamar’s condition remains the same,” and he is still using a walker during his rehabilitation.

And as Kardashian remains by Odom’s side, the way to get through this ongoing process of recovery – as much for herself as for her ex – is to look toward the future.

“Khloé is so looking forward to this year being over: 2015 was a hard one to say the least,” says the source close to Kardashian. “She feels like the new year will bring new things, and she certainly deserves it.”