I’ve seen some instances where only the verb is said and “it” is implied. For example, just saying “J’aime” to say “I like it”. Are there any other times where you can leave it off like this and it’s implied?
Both French and English can have ∅ objects when they're indefinite (Ils embauchent/ they're hiring, je mange là/I'm eating right now, etc).
French also allows ∅ objects when they're generic, while English doesn't. When the object refers to a specific thing, the weak pronouns le/la/les are heavily favoured:
Les pâtes, j'aime beaucoup (ça) (I like pasta a lot -in general)
Tes pâtes, je les aime beaucoup (I like your pasta a lot)
This generic object can be human :
Tu ∅ fais chier !
Le beau temps ∅ invitait à la paresse
As you can tell from the above examples, the ∅ pronoun alternates with the strong pronoun "ça", with identical meaning, when the referent is a non-human.
Note that a more specific object can be coded as generic for a stylistic effect. For example, when offered the last room in a hotel, you may answer "je prends" (I'll take it) despite the object being this very specific last room. Doing so backgrounds the object (which isn't really relevant because no choice was offered) in favour of the action (the agreement to the deal) which is the really relevant part. Likewise, you can hand a book to someone and tell them "lis" (instead of the expected "lis-moi ça" if the focus is on the order to read
Whether ça or ∅ is used depends a lot on the verb. Some generalisations can be given, but they won't give a full overview:
with perception or psychological verbs, ∅ is favoured: je vois, j'entends, je pense, j'imagine.
with verbs of action, ∅ will be favoured for a generic meaning, and most "ça" will be demonstrative.
Additionally, there exists verbs which break the rules outlined above. For example, "je sens" can only mean "I smell" or "I smell it" while "je le sens" is required if the intended meaning is "I feel it".
It's not very common to say J'aime alone in French.
We'd rather say :
J'aime bien, J'aime ça, Ça me plait.
We never use Je l'aime as I like it, but as I love him / her
Aimer is a complex word in French, since it can have a lot of meanings.
But in French we translate it as le / la. And don't find any other example where we don't do it.