Joebass said:So when a diploid bulb is converted to tetra it essentially has two identical sets of chromosomes from each original parent
Yes, when a tetraploid conversion is successful, the make up of the original sets of chromosomes stay intact. they do not recombine in different fashions as they do with sexual reproduction.
Just in case other readers might get the wrong idea, one cannot physically change a lily bulb from diploid to tetraploid. The process changes a cell (or cells) from diploid to tetraploid, and that cell (or cells) continually divides to produce a new tetraploid bulb (or bulbs).
Joebass said: but the seedlings from such could be a whole different range of possibilities, right?
Yes, remembering that tetraploids are still normally self infertile and that said tetraploid would need to be crossed with a compatible mate, the greater number of chromosomes leads to many more possible combinations. I don't know if the relationship is necessarily logarithmic, though.