I suppose it might depend on the dialect of English (I am from the United States), but to me at least, there is a difference in this context- "invite out" to dinner would imply that the dinner will be in a restaurant. In contrast, "invite" to dinner is ambiguous- the dinner could be in a restaurant but also it could be homemade and the invitee is just being invited to the inviter's house.
The Romance languages (including Italian), unlike many Germanic languages (like English) and other languages of the world, do not have neutral gender pronouns- in other words, there actually is no direct equivalent word for "it" in Italian- everything (even inanimate objects) are either "him" or "her." In this particular sentence, the "lo" is translated as "him" rather than "it" because of the context (i.e. usually we can assume that the recipient of an invitation is a person). If the sentence were "Lei lo vuole vedere" then there would be more room for interpretation because "vedere" is just "to see" (and things that are "seen" are not limited to people), so the "lo" in the sentence could refer either to a male person or to a grammatically masculine singular noun (e.g. "libro," "cappello," "albero," etc.)- if the former, then the translation would be "She wants to see him"; if the latter, then "She wants to see it." Hope that helps.
Pardon my poor familiarity with these matters, but I read somewhere that most indo-european languages originally had only a 'neuter' and a 'common gender', of which the common gender later branched into masc. and fem. grammatical genders. In this light, I find it surprising if romance languages do not have a neuter pronoun. I'd be glad if anyone could shed some light on this.
Early PIE originally had two genders; animate and inanimate, the only difference between them being the inanimate nominative was identical to the accusative. Over generations after Tocharian and Anatolian had split off, the core PIE languages had a suffix -a that was used for abstract mass nouns. This later was generallized to collective nouns, and became the neuter plural. But it also was used for a number of singulative words that were often animate, such as verbal nouns or abstract nouns, including verbal nouns. This created the -a declension feminine nouns.
With the additional complication that there were differences between nouns that ended in a vowel or a consonant, that meant Latin had 5 declensions: -a, -us/-um, -(e)s, -ūs (basically, ending on PIE kw- -like clusters), and -ēs (same, but < PIE -y-). The consonant declensions reflect the earlier state of things; masculine and feminine were identical, while m/f and neuter were identical except only in the nominative, which for neuter nouns looked accusative.
By late Latin the -m of the accusative of basically all the nouns turned to a nasalization that wasn't always pronounced. Most romance languages to the north and west (mostly just not Romanian and its sisters) merged the nominative and accusative cases in that process; STELLA, STELLAM > stella; PORTUS, PORTUM > porto; , CANEM > cane.
This meant there were the 'athematic' consonant declensions that were identical in all declensions, and the 'thematic' vowel declensions differed mostly by -o, -a, and an -o that turned into a singular-looking -a in the plural. So there were grounds to reinterpret the neuter as a masculine that became feminine in the plural, which happened in some cases; some Italian words still do that (l'uovo > le uova)
Most Romance languages did some reinterpreting of gender on semantic or phonological grounds. Late Latin was probably something like 1/3 each neuter, feminine, and masculine nouns, but since masculine and neuter merged outside Romanian, that made nouns about 2/3 new-masculine 1/3 feminine. Partly because of this imbalance, partly because it's easier to go on analogies to other things, and partly because it's important to realize that the neuter plural looked like the feminine singular which was confusing, partly because the common-gender 3+ declensions had one pattern for each masculine-feminine-neuter, most languages fixed the neuter words to be masculine.
The long story short is "it" looks like "him" because it pretty much always has, even when they meant different things.