可愛らしい vs. 可愛いらしい
An important thing to note is that when you have an i-adjective the suffix rashii replaces the -i ～い ending, but the auxiliary adjective rashii does not replace the -i ending.
Depending on whether the ending is replaced or not, the function of rashii differs. When it's a suffix, it means something like "-ish" or "-ly". When it's an auxiliary adjective, it's probably expression an assumption, something that you heard from someone, etc.
- kawaii 可愛い
- kawaii rashii 可愛いらしい
It seems that it's cute.
I heard it's cute. (auxiliary adjective.)
- kawai-rashii 可愛らしい
Cute-ish. Lovely. (suffix.)
Actually after looking into it. The question is actually more interesting that it seemed to be at first. らしい can have two meanings: "I heard/it seems" and "-ly/-like". That doesn't change and everything that is usually explained in textbooks is still true.
The meaning 1 "seems" is used when らしい is placed after a full clause, so after a copula, conjugated verb or adjective with the い.
It seems like a typhon is coming tomorrow.
It seems like the weather will be nice on Monday.
He seems to have amassed a lot.
The meaning 2 "-y/-like" normally only attaches to nouns.
A summer-y summer (a real summer, a summer that does what we expect from a summer)
可愛らしい is using the second meaning, but the thing is that we treat 可愛 like a noun. We removed the い and it became a noun. But you can't do that with just any adjective, actually only a small number of adjectives can do that.
For that reason, even though we can understand the meaning from the original adjective, the compound adjective-stem + らしい is actually listed as a separate entry in most dictionaries.
So even though the construction is very very similar to the noun + らしい grammar point, you can also think about them as separate word entirely.
All examples sentences are from Weblio.