case
The word is "tiptoe."
The homograph word for "lame walk or step" is "limp." It can refer to both a limping gait or a weak or unconvincing argument.
What is the homograph for a noisy fight
A homograph for "lame" meaning to walk with difficulty could be "lame" meaning unconvincing or unsatisfactory. Both words are spelled the same but have different meanings.
Laredo - 1965 Walk Softly 2-25 was released on: USA: 31 March 1967
limp
Since "softly" is a word to describe something, it is usually used like this: "The young girl laid the kitten on the pillow softly." Words ending in "ly" can usually be placed anywhere in the sentence... *(But it depends on how it sounds)
LIMPThe grocer's shop only had a few limp lettuces left.Before I had that operation on my knee I could only walk with a limp.
limp
Pussycats walk very softly, so this phrase means to approach a subject softly and circumspectly instead of head-on.
Walk softly, carry a big stick
I'm pretty sure it's, "Speak softly and carry a big stick;" by Theodore Roosevelt.