Is mind the most valuable thing according to the Lord Buddha?

In Buddhism the Mind you refer to is Consciousness or Vinnana in Pali. Please refer to the word Vinnana in the e- Buddhist Dictionary by Ven Nyanatiloka https://www.budsas.org/ebud/bud-dict/dic_idx.htm

Is mind the most valuable thing according to the buddha that we should protect by doing 
anything to everything?

It's hard to rank dhamma teachings in terms of importance, as they are interrelated in a rather complex way.

I'd argue that renunciation (nekkhamma) or our intentions (cetana and kamma) is more important than protecting the mind, but on the other hand these are more or less associated principles.

Someone else will likely say that another aspect of dhamma is the chief principle. This can be confusing, and hence it is important to find out what is needed for oneself in ones personal practice.

Are there any metaphors said by Lord Buddha on the value of protecting the mind vs doing 
other things?

There is for instance the metaphor from SN35.245, where sati is likened to a gatekeeper in a city:

“So too, bhikkhu, those superior men answered as they were disposed in just the way their own vision had been well purified. “Suppose, bhikkhu, a king had a frontier city with strong ramparts, walls, and arches, and with six gates. The gatekeeper posted there would be wise, competent, and intelligent; one who keeps out strangers and admits acquaintances. A swift pair of messengers would come from the east and ask the gatekeeper: ‘Where, good man, is the lord of this city?’ He would reply: ‘He is sitting in the central square.’ Then the swift pair of messengers would deliver a message of reality to the lord of the city and leave by the route by which they had arrived. Similarly, messengers would come from the west, from the north, from the south, deliver their message, and leave by the route by which they had arrived.

“I have made up this simile, bhikkhu, in order to convey a meaning. This is the meaning here: ‘The city’: this is a designation for this body consisting of the four great elements, originating from mother and father, built up out of boiled rice and gruel, subject to impermanence, to being worn and rubbed away, to breaking apart and dispersal. ‘The six gates’: this is a designation for the six internal sense bases. ‘The gatekeeper’: this is a designation for mindfulness. ‘The swift pair of messengers’: this is a designation for serenity and insight. ‘The lord of the city’: this is designation for consciousness. ‘The central square’: this is a designation for the four great elements—the earth element, the water element, the heat element, the air element. ‘A message of reality’: this is a designation for Nibbāna. ‘The route by which they had arrived’: this is a designation for the Noble Eightfold Path; that is, right view … right concentration.“

https://suttacentral.net/sn35.245/en/bodhi

Is mind the most valuable thing according to the buddha that we should protect by doing anything to everything?

Are there any metaphors said by Lord Buddha on the value of protecting the mind vs doing other things ?

While 'valuable' might not be the best term for it has to operate in conjunction with various components in the chain of dependent origination, there's no doubt mind plays such a vital role among them:

Mind precedes all mental states. Mind is their chief; they are all mind-wrought. If with an impure mind a person speaks or acts suffering follows him like the wheel that follows the foot of the ox.

Mind precedes all mental states. Mind is their chief; they are all mind-wrought. If with a pure mind a person speaks or acts happiness follows him like his never-departing shadow. ~~ Dhp 1 ~~

Not valuable, but most important..it is the basis of his dhamma...also mind is hurdle in buddhist practice and mind itself is the cure...by crossing this mind -realm one attain goal of buddhism: nibbana..which cant be conceived by this mind..only one word to describe that state : unconditional happiness

From Dhammapada

184 "Nibbana is supreme," say the Buddhas.

---

43 Neither mother, father, nor any other relative can do one greater good than one's own well-directed mind.

In MN 56, we see disciples of the founder of Jainism, Mahavira (called Nigantha Nataputta in the suttas) debate with the Buddha.

Apparently, Nigantha Nataputta taught that physical deeds weigh more heavily than mental deeds.

“Reverend Gotama, Nigaṇṭha Nātaputta doesn’t usually speak in terms of ‘deeds’. He usually speaks in terms of ‘rods’.”

“Then how many kinds of rod does Nigaṇṭha Nātaputta describe for performing bad deeds?”

“Nigaṇṭha Nātaputta describes three kinds of rod for performing bad deeds: the physical rod, the verbal rod, and the mental rod.” .....

“Of the three rods thus analyzed and differentiated, which rod does Nigaṇṭha Nātaputta describe as being the most blameworthy for performing bad deeds: the physical rod, the verbal rod, or the mental rod?”

“Nigaṇṭha Nātaputta describes the physical rod as being the most blameworthy for performing bad deeds, not so much the verbal rod or the mental rod.”

What did the Buddha teach?

“Tapassī, the Realized One doesn’t usually speak in terms of ‘rods’. He usually speaks in terms of ‘deeds’.”

“Then how many kinds of deed do you describe for performing bad deeds?”

“I describe three kinds of deed for performing bad deeds: physical deeds, verbal deeds, and mental deeds.” .....

“Of the three deeds thus analyzed and differentiated, which deed do you describe as being the most blameworthy for performing bad deeds: physical deeds, verbal deeds, or mental deeds?”

“I describe mental deeds as being the most blameworthy for performing bad deeds, not so much physical deeds or verbal deeds.”

And later the Jain householder Upali came to debate with the Buddha.

When he said this, the householder Upāli said to him, “Good, sir, well done by Tapassī! The honorable Tapassī has answered the ascetic Gotama like an educated disciple who rightly understands their teacher’s instructions. For how impressive is the measly mental rod when compared with the substantial physical rod? Rather, the physical rod is the most blameworthy for performing bad deeds, not so much the verbal rod or the mental rod.” .....

“What do you think, householder? Take a Jain ascetic who is restrained in the fourfold restraint: obstructed by all water, devoted to all water, shaking off all water, pervaded by all water. When going out and coming back they accidentally injure many little creatures. Now, what result does Nigaṇṭha Nātaputta say they would incur?”

“Sir, Nigaṇṭha Nātaputta says that unintentional acts are not very blameworthy.”

“But if they are intentional?”

“Then they are very blameworthy.”

“But where does Nigaṇṭha Nātaputta say that intention is classified?”

“In the mental rod, sir.”

“Think about it, householder! You should think before answering. What you said before and what you said after don’t match up. But you said that you would debate on the basis of truth.” ......

“Sir, I was already delighted and satisfied by the Buddha’s very first simile. Nevertheless, I wanted to hear the Buddha’s various solutions to the problem, so I thought I’d oppose you in this way.

Excellent, sir! Excellent! As if he were righting the overturned, or revealing the hidden, or pointing out the path to the lost, or lighting a lamp in the dark so people with good eyes can see what’s there, the Buddha has made the teaching clear in many ways. I go for refuge to the Buddha, to the teaching, and to the mendicant Saṅgha. From this day forth, may the Buddha remember me as a lay follower who has gone for refuge for life.”

And using this simile and other similes, the Buddha convinced Upali that mental deeds weigh more heavily than physical deeds and verbal deeds. Thereafter, Upali became a Buddhist.