"focus lies" vs "focus lays"

It's a lie-lay conundrum. Transitive vs. intransitive.

Your first example is grammatically incorrect and should read:

Our focus lies on the electronic and mechanic sectors.

Your second example is correct.

A transitive verb takes a direct object.

In "I like fruits" and "she makes cakes," the verbs "like" and "makes" are transitive.

An intransitive verb does not take a direct object.

In "she spoke softly" and "I run fast," the verbs "spoke" and "run" are intransitive.

Lay is transitive, takes an object. For example: "She laid the notebook on the table."

lay

to place (someone or something) down gently in a flat position

Note the tenses of lay: “lay, laid, laid” (to place or put down)

Lie is intransitive, does not take an object. For example: "My dog lies here." "She lay unconscious on the bed." The past tense of lie is lay.

lie

to be located in a particular place

Tenses of lie: “lie, lay, lain” (to recline or remain)

There are many verbs which are both transitive and intransitive.

For example: "She has been singing all day." "She has been singing the same song all day."

I've spent my life listening to "'Lie', not 'Lay'" and its ever so pleasant variations. Here it is clearly "focus 'lies' not 'lays'".

I delight in the distinction of Transitive over Intransitive but the problem here is also usage and consistency.

The meaning of "Our focus lies on the electronic and mechanic sectors." is that the focus is already there, is there currently. This is distinct from the mistaken usage; "Our focus lays there." which would mean our focus is in action, on the way to being there. Painful and quite incorrect for this sentence. Laying describes an action, not a static condition.

More important (what I forgot) is the fact that the expression being used has no physical reality. Whether the focus lays or lies is not the point of the sentence. Focus here means The emphasis of our various sectors. The physical nature of transitive or intransitive matters only by way of habit. In this case the habit of our Usage of the terms. According to the numbers 'Lies" is still in the lead.

Such common usage would account for your millions being 573 to 72 give or take. My Mother will get back to each of those poor 72 mil.