Doesn't Thekla's have the stouter bill? I found this birdforum thread that goes into a lot of depth on the various differences, and even with that info it is often still not easy because of variations in individual birds. So I feel a little better about not knowing for sure.
I believe you're mixing convex and concave. Convex = curved outward Concave = curved inward http://www.merriam-webster.com/dictionary/convex http://www.merriam-webster.com/dictionary/concave The lower mandible on a Thekla Lark is curved outward, so it's convex.
www.birdforum.net
Attached below is a photo from the Ebro delta where this thread and guides told me that there are no Thekla's larks. I suppose the bill is a tiny bit longer than in the first link I posted, but it is not at all easy to be sure. I hadn't read that 'plain' face == Crested, but this one doesn't seem to have a 'plain' face.