I am wondering if there are any other non-bacterial sources of LPS. To my understanding, lipopolysacchrides (LPS) are components of the outer leaflet of gram-negative bacteria, but are there any other sources of LPS such as fungi?.
Yes, there is.
Lipopolysacchrides have been found in eukaryotes. The most famous example is green algae from Genus Chlorella.
According to Armstrong et al., (2002):
The lipopolysaccharides (LPS) are ubiquitous components of the outer leaflet of the outer membrane of all gram-negative bacteria and are the principal toxic products of these organisms (1). The membrane anchor of LPS is lipid A, a central phosphodisaccharide unit that is attached to multiple -hydroxy fatty acid chains. LPS also contains the novel sugar, 3-deoxy-D-mannooctulosonic acid (KDO). Although generally believed to be restricted to prokaryotes, specifically the gram-negative eubacteria and the cyanobacteria (2), an LPS-like molecule has recently been reported from a eukaryote, the green alga Chlorella sp., strain NC64A. (emphases mine)
Also, for further discussion on LPS in eukaryotes, please see Histochemical Evidence for Lipopolysaccharide (Endotoxin) in Eukaryotes.