Can someone explain this line in “Come Ye Sinners?”

I love this hymn, but I have trouble understanding this part:

1 Let not conscience make you linger,

2 Nor of fitness fondly dream;

3 All the fitness He requires

4 Is to feel your need of Him.

I’m assuming the first line means don’t be led astray by your own desires and temptations. I’m confused about the rest of it though. What does “fitness” mean in this context?

I also thought the last fine said “FILL your need,” and not “feel your need.” Now I’m even more confused, but every site I looked on agrees these are the words.

Thanks!