It usually scorches the leaves so they just shrivel up and drop off. The plant then just looks unsightly and sorry for itself - not what you would want for the front of your house. You could try them however and see if they cope.
Whatever you put there will need a lot of water. You can help by giving the plants as large a container as you can. Bear in mind that lavender would naturally live in crevices among rocks so its roots would not be so prone to drying out.
I think you'd probably get away with some of the hebes that have thicker leaves. I had Hebe x franciscana 'Variegata' on my windowsill until it outgrew the pots. It wilted if I wasn't quick enough with the watering, but it came back well.
Other plants you might like, and that would work well in this situation and with each other, would be Cistus and rosemary.
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I think you'd probably get away with some of the hebes that have thicker leaves. I had Hebe x franciscana 'Variegata' on my windowsill until it outgrew the pots. It wilted if I wasn't quick enough with the watering, but it came back well.
Other plants you might like, and that would work well in this situation and with each other, would be Cistus and rosemary.