Analysis:
This quatrain by Saadi Shirazi expresses a profound sense of devotion and humility. Let's break down each line:

Line 1: من گر سگکی زان تو باشم چه شود؟

"What harm if I were but a dog of your household?"
The speaker expresses a willingness to be in the lowest position, even that of a dog, as long as they are associated with the beloved.

Line 2: خاری ز گلستان تو باشم چه شود؟

"A thorn in your rose garden, what would that be?"
Here, the speaker compares themselves to a thorn in a rose garden, a seemingly negative thing. However, the implication is that even as a thorn, they would be close to the beauty and fragrance of the roses, which symbolize the beloved.

Line 3: شیران جهان روبه درگاه تواند

"The lions of the world bow at your door,"
This line emphasizes the beloved's power and influence. Even mighty lions, representing powerful figures, bow down to them.

Line 4: گر من سگ دربان تو باشم چه شود؟

"So what if I were your doorkeeper's dog?"
The speaker again expresses their willingness to be in the lowest position, even as a guard dog, as long as they are associated with the beloved.

Deeper Meaning:

This quatrain explores themes of love, devotion, and humility. It suggests that:

Love can be all-consuming: The speaker is so consumed by love that they are willing to accept any position or role, no matter how lowly.
The beloved is idealized: The speaker sees the beloved as a powerful and perfect being.
The speaker is willing to sacrifice everything for love: The speaker is willing to give up their pride and dignity in order to be close to the beloved.

This quatrain is a powerful expression of unrequited love and the lengths to which one might go for the sake of love. It highlights the human capacity for devotion and self-sacrifice.