Hi PradaP,
I'm a brit flying for LH Regional and it was always my dream to fly for LH, so I can understand where you are coming from:-).
Take a look at the posts on the LH Italia thread for information on the DLR tests. You will perhaps already know that the test is split into three parts the GU (Stage 1), Sim Ride (Stage 2) and FU/FQ (Stage 3).
As a non-native speaker I think you would find it very difficult to get into LH itself. Nevertheless they are recruiting and if you fit the requirements (under 34 and with good eyesight) then you might want to give it a try. However, the pass rate (for Germans) is around 10% so you'll have to be prepared to be disappointed.
IMHO you should probably try Cityline. They are wholly owned by LH although not part of the LH KTV(Common Labour Agreement) so you would be restricted to flying up Emb 195 size aircraft at the moment.
The recruitment process for similar CLH (Cityline) is more or less the same as LH but they should allow you to take the GU in English (as you have seen from the above answer, Stage 2 and 3 are in German). There are a lot of foreign nationals at CLH and they have been recruiting heavily over the last few years. They did have an age restriction of 38 but removed it recently. Not sure if it is back in force again. Beyond Cityline, the other LH Regional partners Eurowings, Contact Air and Augsburg Airways would also be possibilities. The last two are independent companies but almost fully integrated into LH as far as perks and operations go (but sadly not salary!)
Regarding DLR the basic rule is that to fly under a LH callsign in Germany you need Stage 1 and 2 at least. Stage 3 is needed for CLH, , LH Italia, LH Cargo, Germanwings and. of course, LH itself. The odd one out is Condor, who are also recruiting, and don't require DLR as they have now split from LH.
As to the pass rate, it obviously varies but as a rough guide, 40-50% pass stage 1, most people seem to pass the sim (?) and the the success rate at stage 3 is closely related to the state of the market (although no one will admit this), so it has been very low but is likely to improve as the number of qualified pilots on the market falls.
The bottom line is that, at present, if you want to work in Germany you really need the DLR GU (Stage 1) at least. There are virtually no jobs worth having outside the LH world as Air Berlin seem to be up to strength and any shortfalls are likely to be filled by the demise of Hamburg International last week.
Good luck if you decide to try. It's a long road but worth it if you succeed. LH are every bit as ruthless as Ryanair when it comes to letting people go, but if you can hang onto your job there are a lot of good perks and it's generally a nice place to be.
All the best,
KT