The low fertility of triploids is both on the pollen and on the pod side usually. But every triploid cultivar is likely to be different. When one crosses a diploid with a tetraploid in either direction or a triploid with a diploid in either direction or a tetraploid with a triploid in either direction pods will be set at the typical percentage for the pod/pollen parent combination. As an example, If diploid 'Pardon Me' pollinated with diploid 'Barbara Mitchell' pollen sets a pod 8 out of 10 times (80%) then diploid Pardon Me pollinated with tetraploid Barbara Mitchell will set a pod 8 out of 10 times. Even if the two parents have different ploidies the crosses 'take' and set a pod relatively normally. The problems rear their heads slightly later - within seven to ten days most of the pods will abort. A few will linger on and appear to develop but abort later and a very few will manage to develop for five weeks or more. Most of those will show wrinkled collapsed sections or compartments. When opened they are likely to have only one or two mature looking seeds at best, most will not have any good seeds. Triploids typically produce a lower proportion of viable pollen/ovules than diploids or tetraploids but should be consistent in the same growing conditions (temperature being most important).
Yes, specific crosses that manage to keep their pods developing for the longest are likely to be consistent. What Arisumi did was look to see which crosses kept their pods for more than a week and then concentrated on repeating those crosses.
Triploids do have three sets of chromosomes. Their pollen will be many different sizes because each pollen grain is likely to have a different number of the 33 chromosomes. A diploid with 22 chromosomes has a working method of producing pollen with exactly 11 chromosomes (one from each of the 11 pairs). A tetraploid has a partially working method of producing pollen with 22 chromosomes (a pair for each of the 11 quadruples). Pollen from tetraploids may not be exactly 22 chromosomes due to errors in pairing during its production. But triploids have an extremely error prone pollen production. Triploid pollen can have anything from 11 to 22 chromosomes. Each triploid cultivar may have a different average number of chromosomes in its pollen and a different range of chromosome numbers.
When a triploid is crossed with a diploid successful offspring will be produced when the triploid's pollen (or ovule) has exactly 11 chromosomes to produce a diploid or if by chance it has exactly 22 chromosomes to produce another triploid.
When a triploid is crossed with a tetraploid successful offspring will be produced when the triploid's pollen (or ovule) has exactly 22 chromosomes to produce a tetraploid or if it has exaclty 11 chromosomes to produce another triploid.
Some triploids may be almost completely sterile. Other triploids might have reasonable fertility with tetraploids but be almost completely sterile with diploids or vice versa. 'Garnet Robe' was apparently reasonably fertile with tetraploids but sterile with diploids. When crossed with tetraploids there were four pods successfully set out of ten pollinated flowers and nine seedlings were produced (8 tetraploids and 1 triploid) in total. There are seven diploid offspring registered in the AHS database as having Garnet Robe as a parent.
Temperature at the time that pollen (or ovule or more properly gamete) is produced has an effect on how many errors occur and therefore the number of chromosomes in the pollen grains. Daylily pollen is actually produced many weeks before the flower opens (possibly months before). So whether diploid-triploid crosses produce viable seedlings may depend on when and where the crosses are made - first bloom period, rebloom period, in the garden, in the house, in a greenhouse, etc.
