This verb first appeared in the Quenya Verbal System (QVS) from 1948 as an example of ya-formative half-strong verb ᴹQ. siry(a)- “flow” (PE22/114), though its primitive form ᴹ✶siryă “flow smoothly” appeared a bit earlier in Quendian & Common Eldarin Verbal Structure (EVS1) from the late 1940s (PE22/98). This verb may have replaced the basic verb ᴹQ. sir- “flow” from The Etymologies of the 1930s (Ety/SIR), but see Conceptual Development below.
The verb sirya- continued to appear [albiet without translation] as an example of half-strong verb conjugation in Tolkien’s writings in the 1960s with a past form sirinye (PE17/77; PE22/164). In one place he conjugated it as a weak verb from primitive ✱siryā with weak past siryane (PE22/156), but this may have been a transient or experimental idea.
Conceptual Development: QVS from 1948 has a present-tense form síra as part of the sentence númen Endorello isse sí Vaia síra “westward of Middle-earth where now Ocean flows” (PE22/126). It is not entirely clear which verb it is the present tense for. It looks like the present tense of the basic verb ᴹQ. sir- “flow” from the 1930s, but could have been intended to be the present of the sirya- “flow” instead, since that is the verb for “flow” everywhere else in QVS.
Based on the discussion of half-strong verbs QVS, I would expected the present tense of sirya- to be the long imperfect ✱siryalya; compare the present imperfect taltalya “am slipping down” for half-strong talta- (PE22/115). Such long imperfects were used for the present tense of verbs with otherwise defective presents, the main example being a-verbs such as fara- “hunt” whose present was faralya “is hunting” (PE22/116). But Tolkien also said “some verbs make a strong present, so ōla-, is growing [from ola-]”. Thus síra might be an example of such a strong present for half-strong sirya.
Neo-Quenya: For purpose of Neo-Quenya, I would assume sirya- was the most common Quenya verb for “to flow”, conjugated as a ya-formative half-strong verb. I would further assume that, like in EVS1, sirya- has the implied meaning of “flow [smoothly]”. However, I would assume ᴹQ. sir- is a less commonly used verb for “flow”, especially applicable when flows are turbulent or not continuous, as in the “the Ocean is flowing [síra]” in the sentence given above. For example, Helge Fauskanger used sir- “flow” in his NQNT (NQNT).
The verb lut- “float” appeared in its unaugmented perfect form lútie “have floated” in a draft of the poem Löa Yucainen from 1958 (CPT/1296). It is clearly based on the root √LUT “float” (VT42/18). It also appeared in the final version of the poem within a longer verb form valutie “have flowed away” (CPT/1298), with a prefix va- “away” likely derived from √WA of the same meaning.
Conceptual Development: The Qenya Lexicon of the 1910s had ᴱQ. lutta- or lutu- “flow, float” under the early root ᴱ√LUTU (QL/57). The verb lut- reappeared in Early Qenya Word-lists of the 1920s, where it was translated “float, sail” (PE16/134). Forms of lut- also appeared in the Oilima Markirya and Earendel poems from around 1930, respectively translated as “leave” and “sailed” (MC/213, 216), the gloss “leave” probably being a loose translation.
Neo-Quenya: The root ᴹ√LUT was glossed “float, swim” in The Etymologies of the 1930s (Ety/LUT), so many Neo-Quenya writers use lut- for “swim”, such Helge Fauskanger in his NQNT (NQNT). I would use lut- for “flow” only for something flowing on or within water or some other (possibly metaphorical) substance; for the flowing substance itself I would use other verbs like sirya-. I would also use lut- “sail” only to describe the motion of the ship itself, and for the act of sailing a ship I would use kiryasta-; see that entry for discussion.