I can't really speak on liliums yet but with various other plants there's a lot of factors that would still apply like
diploid vs tetraploid
with diploid you have 4 outcome possibilities per gene pair, with tetraploid you have 16...so just by virtue tetraploid lends itself to requiring more to get a full range of outcomes (it's just a pity that tetraploid often produce less seed)
species vs hybrid
species x species the first gen will be fairly uniform so I'm less inclined to go big numbers with those and will be happy with 10 surviving and then weed those down to the best 3 (from often very minute differences) to make the f2 with...which I will go all out on as that is where really exceptional trait combinations can occur (ie super old paper by the first article
http://mertzdigital.nybg.org/c...
demonstrates, kinda they do use a backcross, that despite the fairly large numbers produced very few of the gladious displayed both day and night scent from the two parent species...if you only did a limited sample there's a good chance you'd probably not encounter it and believe it wasn't possible)
recently tetraploid
if recently tetraploid chances are there's going to be a fair bit of genetic similarity so I don't really feel inclined to do more than 30 - 50...there's differences but also a lot of samey stuff. If you can't tell when in the parentage things were converted to tetraploid though, good chance there aren't a bunch of identical chromsomes (and thus genes) so can see some very unexpected outcomes.
highly mixed parentage qualities vs consistent parentage qualities
plays largely into the previous but as an example the rose Friesia, parents are Friedrich Wörlein and Spanish Sun going back through 4 generations of the parentage everything has a strong or moderate fragrance and everything is either yellow or a light pink, I would expect any cross to produce offspring that is generally fairly similar to each other.
fertility
Some things just have low fertility or germination...like roses where I can easily plant 100 seeds from a cross and be very lucky to get 20 to germinate (or which most or all will have some giant health issue....roses are often luck based flukes as healthy plant + healthy plant = offspring that have extreme mildew issues or rust or blackspot...)
so any combination of those will influence decisions based on the specific cross.