Let's see the context, 2 Kings 4:
18 And when the child was grown, it fell on a day, that he went out to his father to the reapers. 19And he said unto his father, My head, my head. And he said to a lad, Carry him to his mother. 20And when he had taken him, and brought him to his mother, he sat on her knees till noon, and then died. 21And she went up, and laid him on the bed of the man of God, and shut the door upon him, and went out. 22And she called unto her husband, and said, Send me, I pray thee, one of the young men, and one of the asses, that I may run to the man of God, and come again. 23And he said, Wherefore wilt thou go to him to day? it is neither new moon, nor sabbath. And she said, It shall be well.
It was the mother who was suffering. She used the word "well" to her husband because of her faith.
24Then she saddled an ass, and said to her servant, Drive, and go forward; slack not thy riding for me, except I bid thee. 25So she went and came unto the man of God to mount Carmel. And it came to pass, when the man of God saw her afar off, that he said to Gehazi his servant, Behold, yonder is that Shunammite: 26Run now, I pray thee, to meet her, and say unto her, Is it well with thee? is it well with thy husband? is it well with the child? And she answered, It is well.
The 2nd time that she used the word "well", she was replying to Gehazi.
27 And when she came to the man of God to the hill, she caught him by the feet: but Gehazi came near to thrust her away. And the man of God said, Let her alone; for her soul is vexed within her: and the LORD hath hid it from me, and hath not told me. 28Then she said, Did I desire a son of my lord? did I not say, Do not deceive me?
Finally, she confronted Elisha and told him what happened without using the word "well".
The mother was the one who was suffering. She didn't lie to herself, her husband, or Gehazi when she said that it was well. Eventually, Elisha raised her son from death and all was well.
Should we keep saying it is well even when people are really suffering?
Based on this story, there were two conditions:
It was the sufferer who used the word "well".
The sufferer had faith and didn't lie to anyone.
If these two conditions are satisfied, then I think it is okay to say it.