The seeds in one chamber are no more closely related genetically than seeds in different chambers. Each ovule in the pod is genetically different from every other ovule in the same pod.
We get different seedlings, say for flower colour from the same pod (or cross) because daylilies are out-breeding instead of inbreeding. As examples, peas and tomatoes are inbreeding. So if I take the seeds from a Beefsteak tomato and plant them I will get more Beefsteak tomatoes. The seedlings will look like their parent. Basically Beefsteak tomatoes have been pollinating themselves for many generations and have created what is described as a "pure-breeding" line or strain (for characteristics that are important to us the consumers). The same thing happens with peas. If I take the peas from a pod of a purple flowered pea plant and plant them, the seedlings will all be purple flowered just like their parent. That is why Mendel was 'lucky' in the types of plants (peas) he chose to use in his breeding experiments (actually he checked his plants to make certain that they were pure breeding - it was not luck). It is important to know that if I take seeds from a plant that is described as an F1 hybrid or sometimes simply described as a hybrid then the seedlings will not be identical to the parent. Daylily cultivars are basically hybrids. When we hybridize a plant we deliberately force it to out-breed and that has been done with plants such as peas and tomatoes that normally inbreed by self-pollination.
A second reason we can get many different flower colours in the seedlings is that flower colour (and nearly all daylily characteristics we are interested in) are not based on simple genetics. There are probably between 30 and 100 (or more) different genes that influence flower colour. If there was only one gene and there were only two alternative flower colours (say red or yellow) then there would be much less variability in the seedlings from crosses.
As an imaginary example, for a diploid daylily, with only one gene for flower colour (but two chromosomes) and in the simplest case red dominant to yellow, RR is red, Rr is red (and indistinguishable from RR) and rr is yellow. If we cross red x red we might be crossing RR x RR so all the seedlings are red. Or we might have crossed RR x Rr and all the seedlings are red. Or we might have crossed Rr x Rr and approximately three quarters of the seedlings are red and one quarter are yellow.
If we crossed a red with a yellow we might have crossed RR x rr and all the seedlings would be red. Or we might have crossed Rr x rr and approximately half the seedlings will be red and half will be yellow.
But we don't have such a simple case in daylilies. They can be near-white, lavender, pink, purple, yellow, orange, peach, red, etc. The more genes that affect the characteristic, in this case flower colour the more alternative flower colours the seedlings can show (depending on what flower colours the parents show). For some flower colours, usually the lighter colours, there is usually less variability in the seedlings. For example, if we cross one yellow flowered daylily with a different unrelated yellow flowered daylily we expect that all the seedlings will be yellow flowered (more or less - they might vary from near-white, light yellow, or cream, to lemon yellow, etc. depending on the ancestry of both yellow parents). A red flowered daylily might carry the genetics for yellow, and pink or lavender, etc all hidden by the red colour.
If we look at tetraploids the situation becomes even more complicated. Now there are four chromosomes and therefore instead of the simplest diploid case of RR, Rr and rr we now have RRRR, RRRr, RRrr, Rrrr, and rrrr. The genetics becomes very complicated because although RRRR may be red and rrrr may be yellow each one of Rrrr, RRrr and RRRr often may be a different shade of red.
Now back to the original question. yes there are three lobes on the stigma and yes there are three chambers in the pod but there is only one channel in the style through which the pollen tubes grow. The three stigmatic lobes and the three chambers share that channel. So even if one placed pollen from a yellow flower on one lobe and pollen from a red flower on another lobe and pollen from a near-white flower on the third lobe the pollen tubes might cross-over and not grow straight down so that each chamber might produce mixtures of seedlings with different coloured fllowers. We do not know if many of the pollen tubes do grow straight down or how many do since the experiment has not been done and published.
