Lavender is a specific mutant gene. It merely dilutes the pigments.. a black bird gets diluted into lavender or "self blue".. unlike blue, lavender also dilutes red/gold pigments.. one good example of this are Porcelains.. they are just Mille Fleurs with lavender.
To get any lavenders, you have to either have lavenders or birds split for lavender (doesn't look lavender but is carrying the gene 'hidden').
Lavender is recessive so lavender x lavender always 100% lavender. This is the reason sometimes it's called "true breeding blue".
To bring lavender into a breed you have to bring it in from another breed where it is already present (using, of course lavender birds). You would generally choose a breed with as few issues that need to be corrected as possible. You would probably not mix a cochin and a modern game--too different
That said, I believe lavender was first introduced to silkies with OEGB, not as badly aligned as my example of moderns and cochins, but still with a lot of breed issues to correct.
Lavender is a recessive gene and your bird will need to be homozygous(have 2 copies) to display the color. To me this means it should take longer to introduce into your line than some other colors as you wont get any lavender birds until your F2 generation.
In the US, Lavender is called Self Blue sometimes....once your line of birds is homozygous for lavender then it will always breed true( a lav/lav bird mated to a lav/lav bird will produce a lav/lav bird)
This makes it different from blue which is an incomplet dominant meaning it will only express blue in a bird if there is one gene present, two genes will produce spash(you can think of splash as bluer than blue)
Additionally Blue dilutes only black so you get birds with blue and red colors, Lavender Dilutes Black and Red, so it will turn your whole bird into pastel colors.
Sonoran makes a very good point in using lavender birds more closely resembling one's intended new lavender bird goal.. leg feathering is very hard to get completely rid of once crossed in- not a good idea to use lav silkies/cochins for introducing lavender into a clean leg project for sure.
Haha good question, monkey.. don't know for sure but my guess is probably a strange looking buffish colored bird. The brown areas on Mille Fluers kind of look dark to me(don't know their full genotype so I'm not sure if they have gold melaninzers or not) yet they turn straw colored on porcelains.
"Isabel" is kinda close to that idea- it's a lavender over a uh.. buff?(Sonoran, remind me? Or do you know the answer to lavender on a red bird?) bird.