Lacing in any breed is due to a bird being homozygous for the pattern gene, homozygous columbian, and homozygous for melanotic- the E locus can vary and some laced birds carry dark brown.
Blue andalusians have the following genotype.
E/E Bl/bl+ Co/Co (Ml‐Pg)/(Ml‐Pg). or E*E/E*E Bl*Bl/Bl*bl Co*Co / Co*Co (Ml*Ml-Pg*PG)/(Ml*Ml-Pg*PG)
A laced bird is not self-blue because it is laced. Self-blue birds can not be laced. Any bird that has blue feathers and no secondary color patterns is self-blue. A self-blue can be hypostatic black and heterozygous at the blue locus or hypostatic black and homozygous lavender.
Most individuals want self-blue to only refer to lavender birds and historically this was not the case. See my earlier posts or information below.
" These facts have led to the current view that the case involves a single allelomorphic pair of characters. The blacks and blue-splashed represent the homozygous conditions, while the self blue is the heterozygote between the two. When blues are interbred, blacks, blues, and blue-splashed are produced in a ratio approximating 1: 2: 1 for these classes, respectively, which seems to corroborate this view."
"Emphasis has usually been laid on their distinctness from the black and the blue-splashed birds, but it seems important to note their resemblance to these two classes. In the first place, they are like the blacks in being self-colored, that is, all feathers in all parts of the body are pigmented."
I have provided a reference for the paper.
Lippincott, W. A. (1918). The case of the Blue Andalusian. American Naturalist, 95-115.
If blue with lacing is blue and lavender is self-blue then what is blue without a secondary color pattern? It has to have a name. How about blue-not-blue or not lavender/not blue color? I do not think the names will catch on.
I like the three below- they work for me.
black laced blue
self blue
lavender
I have posted all I will post on nomenclature.