I have plenty of Indian colleagues that travel on LH via FRA between the US and India and the common consent is that you should have a transit visa in the described case.

The consulates and embassy in the US are pretty clear about it being the rule and whether you think it is ridiculous or not is a totally different story (some people likely may argue that India's visa rules are also odd & cumbersome).

Of course, enforcement of the rules may not always be done as intended so if you feel you want to chance it then please go ahead, but it is at your own risk. If you want piece of mind better get one or pick a different airline and transit point that doesn't have this build in hassle.