As with EVERY other performer who's experienced a personal tragedy in their life --it doesn't affect them... the show must go on and so do they.
As I've mentioned before on previous threads asking this same question... Audra McDonald was back in the recent revival of 110 IN THE SHADE the day after her father passed away. Marie Osmond was back in DANCING WITH THE STARS two days after her father passed away. Bernadette Peters resumed her concert tour three weeks after her husband passed away. Liam Neeson was back at work on a film two weeks after Natasha Richardson passed away. The list goes on.
I'm sure Ms. Lansbury never missed one performance due to Ms. Arthur's passing.
Betty White, who so memorably played Rose Nylund on The Golden Girls opposite Arthur, gave this statement to Entertainment Tonight: "I knew it would hurt, I just didn't know it would hurt this much. I'm so happy that she received her Lifetime Achievement Award while she was still with us, so she could appreciate that. She was such a big part of my life."
Angela Lansbury, who co-starred with Arthur in Mame on Broadway, released this statement (via ET Online): "Bea Arthur and I first met when we did 'Mame' together in 1965. She became and has remained 'My Bosom Buddy' ever since. I am deeply saddened by her passing, but also relieved that she is released from the pain. I spoke to Matt, her son, yesterday and I was aware that her time was imminent. She was a rare and unique performer and a dear, dear friend."
I heard an interview with her on some red carpet function. She said,"It is always sad when someone passes away...but who the **** is Bea Arthur?" When she was reminded that Ms. Arthur was the woman who recreated her Tony winning role as Vera in the film version of MAME starring the late Lucille Ball, Ms. Lansbury stated, "Oh, HER. Well, now she is not BETWEEN 40 and Death, is she? Who has my cocktail?"