Why is "Fearing the Lord" equated to loving Him? This question is probably more directed an Old Testament pattern of a description of our attitude towards the Lord.  I equate &quot;fear&quot; more closely with &quot;hate&quot;. For example today there was local news that a  mountain lion &quot;may have attacked a pet dog&quot;.  That fear factor would lead to efforts to have the mountain lion killed.  That's pretty far from love.
Let's go an assumption (that I made up) that &quot;fear&quot; were intended more closely to &quot;respect&quot;. That may be the case but one can just as easily respect someone you love as someone you fear.
Are there multiple words/nuances of fear in the Biblical languages (Hebrew? Greek? Aramaic) ?  Similarly are there some aspects of the Biblical Hebrew culture - or even more generally Semitic/Middle Eastern culture - that explains why &quot;fear&quot; is chosen as the way to instruct/describe the attitude/disposition to the Lord?
Shorter answer
Talking about lion, we are to hate our &quot;adversary the devil who prowls around like a roaring lion, seeking someone to devour&quot; (1 Pet 5:8).  But the Fear of the LORD is qualitatively the opposite, as this fear enables us to enjoy and grow in our love for God, the key to our happiness.
Longer answer
I'm attempting to show through examples below, that our everyday use of fear in common English today ALSO carries the nuances of fear that the Biblical authors utilized to render what our attitude to God should be.  Therefore, I think we need not look into specifically Hebrew / Semitic / Ancient Near Eastern culture as to why the Biblical authors chose the word 'fear'.  In this answer I attempt to show how fear can be compatible with love and in fact can help one to deepen the love beyond feelings.
If we analyze semantically, in the Biblical books the fear of the LORD is a key element of loving God, similar to how a child both fears and loves his father, or how a citizen both fears and loves his king, or how a husband both fears and loves his wife.  Of course it has to be a certain kind of fear that can be compatible with love, and not the kind of fear that leads us to hate and want to kill an enemy.
For example, a husband can fear to hurt his wife (example: not being appreciative / aloof, or doing things that his wife hates for good reason).  A citizen can fear to incur the king's just wrath (example: siding with the king's enemy, or oppressing the helpless whom the king protects, or violating laws that the king enacted).  A child can fear to alienate his father's good graces by climbing to reach the cookie jar in a precarious manner (going his own way rather than trusting his father's wisdom).
In all the examples above, the fear is the internal power within us which prevents us from hurting another's feeling, distrusting another's wisdom, disobeying a good rule/law, and damaging the trust and enjoyment of the relationship.  In relationships where there is a natural imbalance of power (such as the child to the father and the citizen to the king), the fear is supplemented by an external force to aid our internal power which in turn prevents us from doing the same things.  For example, the fear to be (justly) punished or the fear that one is at the mercy of the other's power help us from disobeying a (wise) commandment for our own good.
All those aspects of fear are compatible with our love for God, and more specifically for the LORD (Yahweh), the God of the Israelite and the Christian God:

We fear His awesome power (the imbalance between creature and creator)
We fear his (just) discipline for our own good
We fear the curtailing of his blessings if we don't do what we are supposed to do
We fear becoming His enemy: possible since He allows it (we have free will), which will result in our destruction (since He promised to punish the wicked)

All those are external force aiding our internal power of fear of hurting God (He was hurt in Hosea) to prod us into living in the right path so we can enjoy more fully our loving relationship with Him.  This force also motivates us to obey God's wisdom reflected partly in his commandments so we do not go into dangerous areas outside the right path, just like the child who has been told not to climb the cupboard to reach the cookie jar.
IN CONTRAST, fear for demons (God's enemy) which is similar to fear of natural enemies (like your lion example, criminals, terrorists) is NOT compatible with love since this fear DOES lead to hate and move us to kill them.  This fear is qualitatively different and leading us into alarm, anxiety, and defensive posture rather than into alertness, safety, and openness:

We fear their superior knowledge and power over the natural which they use to deceive us (Satan is the Father of lies)
We fear their persistent hate toward the human race (like how we fear Sauron in the Lord of the Rings)
We fear our falling into temptation which then damages our love for God and for our loved ones

CONCLUSION: God wants us to fear Him in love, by graduating FROM merely the fear of external forces of the power imbalance or of punishment TO the healthy internal fear resulting from our humility (of being creature), respect (of God being wiser), and desire for happiness in our loving relationship with Him.  Bottom line: we fear damage to our own happiness, which can only be found in our love for God, which needs to include fear of the LORD.
The book of Proverbs (wisdom for living) has these verses to highlight various aspects of this healthy kind of fear (see other verses, including from other books, here):

Fear leads to trusting God's wisdom and discipline Prov 1:7: Fear of the Lord is the foundation of true knowledge, but fools despise wisdom and discipline.
Fear acknowledges God's power to determine short/long life Prov 10:27: Fear of the Lord lengthens one’s life, but the years of the wicked are cut short.
Fear prods us to walk only in the right paths leads to our security, refuge, and protection:

Prov 14:26-27: ²⁶ Those who fear the Lord are secure; he will be a refuge for their children.  ²⁷ Fear of the Lord is a life-giving fountain; it offers escape from the snares of death.
Prov 19:23: Fear of the Lord leads to life, bringing security and protection from harm.
Prov 14:2: Those who follow the right path fear the Lord; those who take the wrong path despise him.


Signs of those who fear to obey God's commandment:

Coveting only God: Prov 23:17: Don’t envy sinners, but always continue to fear the Lord.
Truth, integrity, humility Prov 8:13: All who fear the Lord will hate evil.   Therefore, I hate pride and arrogance, corruption and perverse speech.