What is the role of lamellar bodies in lung cells?
Well, The paper published in Nature 2003:

Despite two decades of progress in understanding the role of LGs and
their contents in epidermal barrier function, almost nothing is known
about the mechanisms responsible for the assembly of these unique
organelles.source: http://www.nature.com/jid/journal/v120/n4/full/5601763a.html

Since then the word &quot;Lamellar Granule&quot; appeared only 5 more times in journals:

1: Sando GN, Zhu H, Weis JM, Richman JT, Wertz PW, Madison KC.
Caveolin expression and localization in human keratinocytes suggest a
role in lamellar granule biogenesis. J Invest Dermatol. 2003
Apr;120(4):531-41. PubMed PMID:
12648214.
2: Akiyama M. The roles of ABCA12 in epidermal lipid barrier formation
and keratinocyte differentiation. Biochim Biophys Acta. 2014
Mar;1841(3):435-40. doi:
10.1016/j.bbalip.2013.08.009. Epub 2013 Aug 15. Review. PubMed PMID: 23954554.
3: Sakai K, Akiyama M, Sugiyama-Nakagiri Y, McMillan JR, Sawamura D,
Shimizu H. Localization of ABCA12 from Golgi apparatus to lamellar
granules in human upper epidermal keratinocytes. Exp Dermatol. 2007
Nov;16(11):920-6. PubMed PMID:
17927575.
4: Lee WS, Oh TH, Chun SH, Jeon SY, Lee EY, Lee S, Park WS, Hwang S.
Integral lipid in human hair follicle. J Investig Dermatol Symp Proc.
2005 Dec;10(3):234-7. PubMed PMID: 16382672.
5: Kelsell DP, Norgett EE, Unsworth H, Teh MT, Cullup T, Mein CA,
Dopping-Hepenstal PJ, Dale BA, Tadini G, Fleckman P, Stephens KG,
Sybert VP, Mallory SB, North BV, Witt DR, Sprecher E, Taylor AE,
Ilchyshyn A, Kennedy CT, Goodyear H, Moss C, Paige D, Harper JI, Young
BD, Leigh IM, Eady RA, O'Toole EA.  Mutations in ABCA12 underlie the
severe congenital skin disease harlequin ichthyosis. Am J Hum Genet.
2005 May;76(5):794-803. Epub 2005 Mar 8. PubMed PMID: 15756637; PubMed
Central PMCID: PMC1199369.
6: Ishida-Yamamoto A, Deraison C, Bonnart C, Bitoun E, Robinson R,
O'Brien TJ, Wakamatsu K, Ohtsubo S, Takahashi H, Hashimoto Y,
Dopping-Hepenstal PJ, McGrath JA, Iizuka H, Richard G, Hovnanian A.
LEKTI is localized in lamellar granules, separated from KLK5 and KLK7,
and is secreted in the extracellular spaces of the  superficial
stratum granulosum. J Invest Dermatol. 2005 Feb;124(2):360-6. PubMed
PMID: 15675955.

According to the last mentioned paper[6]:

LG(Lameller granule) constitute a specialized secretory system within the epidermis.

LG are seen as isolated oval-shaped granules in post-embedding methods, whereas they appear as parts of beaded tubular structures in cryo-ultramicrotomy

Result highlights the biological significance of LG in regulation of protease activities.

LEKTI labels were aggregated and not evenly distributed throughout the LG system, indicating the heterogeneous nature of the LG  (Ishida-Yamamoto et al, 2004).

Biologically active fragments derived from LEKTI are released extracellularly (Bitoun et al, 2003).

LEKTI labels were seen in the extracellular spaces in the superficial granular layers and the first cornified layer with release from the apical side of upper granular cells. Aggregates of LEKTI immunolabels were also closely associated with the TGN46-positive trans-Golgi network .

Double labeling with antibodies to glucosylceramide, a well-known LG molecule, showed that each occupies a distinct domain of beaded tubular structure

The ultrastructural localization of LEKTI was compared with that of KLK7. As reported previously (Sondell et al, 1995; Ishida-Yamamoto et al, 2004), KLK7 was localized in the LG system but was not co-localized with LEKTI within keratinocytes.

This finding suggests that LEKTI is expressed and released earlier than its target proteases, which is consistent with a role in preventing premature proteolysis of extracellular matrix proteins or cell surface adhesion molecules, and in controlling the timing of desquamation.


Source: [6]. http://www.nature.com/jid/journal/v124/n2/fig_tab/5602696f4.html

(source: nature.com)

Caption: Lympho-epithelial Kazal-type-related inhibitor (LEKTI) is
transported through the lamellar granule (LG) system. Post-embedding
immunoelectron microscopy using Lowicryl HM20 resin (A, D) and a
cryo-ultramicrotomy method (B, C, E). (A, B) LEKTI signals (black
arrows) are detected in the LG using polyclonal antibodies against
D8–D11 in (A) and D1–D6 in (B). Note that LG are seen as isolated
granules in the post-embedding method (A), but appear as beaded
tubular structures in the cryo-ultramicrotomy (B). Lamellar internal
structures are seen in both methods (white arrows). (C) LEKTI is
secreted from the apical side of upper granular cells (arrows). d,
desmosomes. Polyclonal antibody to D8–D11 and desmoglein 1 monoclonal
antibody were used and were labeled with 5 and 10 nm immunogold,
respectively. (D) LEKTI antibody to D8–D11 labels are closely
associated with those of the TGN46-positive trans-Golgi network. (E)
LEKTI (monoclonal antibody, 5 nm gold labels) and glucosylceramides
(GlcCer, 10 nm gold labels) are localized within the same continuous
beaded tubular structure of the LG system.