Since you know kind of where they are, including the ones that are peeking out, it's OK to get to them now. Just be careful digging as you now have not only the bulbs to be careful about, but also any growth that is still underground that can't be seen. After doing that, I would mulch the area. That will hide the digging and also make the new owner think he got some nice mulched area also. You can leave him some surprises, though...maybe some inexpensive seeds of some annual or perennial plant to make up for taking the lilies. To me, it's always fun to see what plants come up at a new house. Who knows, we might see your new owner coming here to help identify some plants.

I think the key for both the tulip and lily is good draining soil. Poor drainage can potentially cause rot in both types of bulbs. The foliage is what technically "feeds" the bulb, although some supplement (good composted materials and perhaps some bulb fertilizer or bone meal) might help build a strong root system. Since your lily is up that tall, it might be better, if possible, to wait until the fall to move it as the stem is dying back. That way you have a better chance at getting a decent bloom next year. Otherwise, if you move, try to dig down deep and be careful of breaking the stem. You might find babies under the soil too.

In both cases, you can move but be careful because there are often offsets directly attached to the mother bulb that shoot up a sprout away from the mother (where the shoot runs horizontally and then abruptly goes vertical. Also be careful not to accidentally break off the shoot under the soil when digging.

The symtoms you describe often happens in low light. have you grown this one in excessive shade or indoors ? Another time which leaves start to die at the bottom and gradually turn brown is when the lily is affected by boytris. This happens most often due to overwatering. It only takes one night for the lily to get affected by the spores. Nutrient burns on the leaf tips is most often due to build up of fertilizer salts and/or very acidic conditions in the soil. A relatively small pot can cause this especially if you water with fertilizer on regular basis (or the potting soil had fertilizer incorporated) and/or drainage is not perfect. In the ground, you can usually offset this by adding a bit of lime to increase the soil pH (higher soil pH will prevent the solubility of the micronutrient metals). Indoors, the use of water with floride (most often found in tap water in USA) can also lead to tip burn. The good news is that your lily is ok. Keep growing it, and then just plant it outdoors after it has finished blooming. It usually correct itself next year if the lily is in the ground. Example of aluminum salts leaf burn on lilium lancifolium