So far it appears 'oselleier' isn't going to be sourced. Perhaps it's from some website or maybe -ier intends to have some grammatical significance -- or perhaps it is attested somewhere in Tolkien's books, but I don't plan on reading 12 plus volumes again just to find out.
Anyway, as I noted, not too long ago I was involved in a discussion about a tattoo with the word sister in it, and so I already had done some footwork here, and here's what I found (checking Etymologies and VT47 at least).
In Etymologies we find the base THEL- and THELES- with a general meaning 'sister'. A base is not a word itself, although sometimes a word will echo it in form. At this stage 'Sindarin' had yet to be invented, and the external precursor of Sindarin was called 'Noldorin' (long story). In this entry we find the words (not all the words are noted here, and please excuse random lack of diacritics):
Noldorin gwathel 'sister, associate' thel 'sister' also muinthel  Quenya seler 'sister' oselle 'sister, associate' onone 'usually' used of blood-kin in Quenya
The entry for the root WO- explains that the o- in o-torno and o-selle means 'together', so the semantic difference appears to be that these forms expressed a togetherness, or 'kinship' not necessarily of blood. This idea seems better expressed in the 'brother' entry under TOR-
'ON [Old Noldorin] wator (wa = together), especially used of those not brothers by blood, but sworn brothers or associates; N gwador.'
In Quenya the o- form again appears, noting toron 'brother' but otorno 'sworn brother, associate' otornasse 'brotherhood', but usually of the blood kinship was onoro.
So Quenya oselle would seem a good word to describe Leelee as a 'sister' in this sense.
But this is Tolkien, who was not against changing his mind
Etymologies was written in the mid to later 1930s and ultimately abandoned sometime after Tolkien began writing The Lord of the Rings. Tolkien would drastically change the history of the language that was to be called 'Sindarin' in his published tale, as well as some points about the language itself (compared to Noldorin). Were any of these words meant to be part of Sindarin or Quenya as Tolkien would later imagine things?
Much later (roughly 1967 -- 1970), when looking at Elvish play names for the fingers, words for 'sister' would again arise. Now the base is NETH-
Note that back in Etymologies the base NETH- carried the meaning of 'young' and was connected to the name Nessa, and in Noldorin we have the words nith 'youth' neth 'young' as well. In this late text Tolkien will explain NETH- as 'fresh, lively, merry' adding that it had a special association with young women. So now we get Sindarin neth 'girl', while various other notes have 'woman, female person'.
But Tolkien changes his mind again, finally arriving at NETH- 'sister'. And thus we have...
Sindarin nith  Quenya né þ a, né sa
The editors of Vinyar Tengwar explain, after noting that Eldarin tolerated homophonous bases if the meanings were sufficiently distinct [as KHAN- in Etymologies means 'understand, comprehend']:
'On the other hand, KHAN 'brother' probably replaces earlier TOR- 'brother' from the Etymologies [just as NETH- 'sister' in HFN probably replaces the Etymologies base THEL-, THELES- 'sister']. Vinyar Tengwar 47, editor's note 61
If so Quenya seler and oselle are out and Quenya né sa is in. Sound preference aside, in my opinion né sa is the safer choice for 'sister' in any case. And as noted hiril is Sindarin; so to keep things Quenya with a dash of Neo-quenya, for 'lady, sister, healer' I would suggest...
Heri Né sa *Nestar
Or without any Neo-quenya:
Heri Né sa Envinyatar ['Healer' but more properly 'Renewer']
Aragorn was called Envinyatar in the books, but this form seems to be gender neutral. Patrick Wynne (member of the Editorial Team who publish Tolkien's linguistic papers) writes:
'Aragorn's royal name Envinyatar 'the Renewer' in the chapter 'The Houses of Healing' (LR:845) -- this latter consisting of en- 're-' + vinya 'new' + -ta causative marker (i.e. envinyata- = 'to make new again' + -r agentive ending.'