Apparently, L has been added to the not eligible fares. Just got a LH paper voucher which already indicates the change. Also saw updates on the website:
The following Lufthansa tickets are not eligible for a Systemwide Upgrade:
•
Tickets in booking codes X, I, R, N, W, S, L, and E
•
Tickets in booking code L and T for intra-Europe flights
http://www.united.com/page/article/1,,53477,00.html
Although it seemed the MP agents were not informed of the change yet, they told me I could still use it on my upcoming L fare LH flights next week. However it says clearly on the voucher that L is not valid, we will see how it goes.