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This article will help with their care: https://www.gardeningknowhow.com/ornamental/flowers/lobelia/lobelia.htm

Well, it would likely be the rabbits before the dog. Rabbits will alos leaves a nice, clean cut on the plants rather than the gnawing, jagged bites from many other animals, like dogs. This article will be of some help in dealing with rabbits: https://www.gardeningknowhow.com/plant-problems/pests/how-to-keep-rabbits-out-of-gardens.htm

How much sun are they getting in the cold frame? Most likely this is sunscald, which is like sunburn in plants. This typically happens to plants that are not acclimated, but can happen to new growth on plants that are in locations that are a bit too sunny for them. If possible, move the plants to a location that is not quite so intense or you can try to shade the area some by placing a large umbrella (or something similar) over it.

It may be an under watering or over watering issue. I would lean towards under watering. Sometimes, the rootball can get dried out and even if you are watering, the rootball may be repelling the water. Try giving the root area an extra good soaking to rehydrate the rootball.

Make sure the plant is getting enough water, especially if just planted. Container plants also require more watering than those planted in the ground, as they're more prone to drying out. They should be water once daily or twice if temps reach 85 F. or more.

Stick your finger into the soil after watering and make sure the water is actually penetrating the soil. Sometimes potting soil can dry out and start to repel water rather than absorb it. If you find this is the case, soak the whole thing in a tub for a half hour or so to force the soil to absorb the water.

Less likely but still possible is that the water is not draining out and the roots are drowning. Check to make sure that the plants are not in standing water.