It is correct. And imho it's better than "I give her...", because in this case no one would (or should, for that matter) use the present simple. It's true that German doesn't have progressive tenses like English, but it absolutely doesn't mean any German present indicative verb can be translated to English using both the simple and progressive tenses; in some cases you could do it, but it would change the meaning, in others you just can't.
Anyways, I've reported as well.
There is no word lhr (LHR) in this sentence, only ihr.
ich is the subject and in the nominative case, and the verb gebe agrees with ich.
So ihr can't be the subject here (in the nominative case), otherwise the verb would have to be gebt (ihr gebt = you (all) give).
meinen Löffel is in the accusative case, so it's the direct object of gebe.
So ihr must be in the dative case as the indirect object of gebe -- the recipient.
And the only thing that ihr (as a standalone pronoun) is the dative case of is sie "she". Thus it must mean "(to) her".
Because ihr is the dative case of the preposition sie which means "she", and so ihr in this sentence can only mean "(to) her".
"you" can be, depending on how many people you are speaking to and how well you know them, one of du, ihr, Sie, and in the dative case (as when they are the recipient of giving) they would be dir, euch, Ihnen. This sentence has none of dir, euch, Ihnen but has ihr instead.
There is no word Loffel.
The sentence contains the word Löffel (if you can't write the ö, replace it with oe: Loeffel).
That word is masculine.
It's also the direct object of the verb geben -- it is the thing that "suffers" or undergoes the giving.
This it stands in the accusative case, and you have meinen Löffel.
meinem Löffel would be dative case.
Both of those can be correct translations, depending on what grammatical case the word is in.
In the nominative case, ihr means "you" (when speaking to several people).
In the dative case, "ihr" means "(to) her"; it's the dative case of sie "she".
There are also other possible meanings, e.g. possessive "her" or "their" (when the word is before a noun, e.g. ihr Vater = "her father; their father").
The word ihr has several meanings, depending on the case it is in and whether or not it stands before a noun.
ihr on its own in the nominative case means “you” (when speaking to several people).
In this sentence, though, the subject is ich: you can see that because ich can only be nominative and because the verb gebe fits with ich but not with ihr as a subject. Thus the word ihr has to be in the dative case in this sentence: the dative form of sie.
The personal pronoun sie "she" has the dative form ihr "(to) her". That doesn't change forms or add endings.
There's also a possessive determiner ihr "her" corresponding to sie "she". That one does add endings depending on the gender, number, and case of the thing which is owned, e.g. ihr Löffel "her spoon" but ihre Gabel "her fork".
But in this sentence, we don't have possessive ihr but rather personal pronoun ihr.
In English, they're the same for "she" (they're both "her") but if you use "he" instead, you'll see a difference: "his spoon" versus "I give him my spoon". You can't say "I give his my spoon".
Also, Ihre (capitalised) is never correct (in the middle of a sentence) for things related to "she, her".