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."
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.
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."