Q: What can LH do to increase your loyalty?

I totally agree that if LH would update their offerings in all lounges, that would definitively would be the most preferable. The problem is that I just don't see that happening, LH is just too stingy (and that is also what makes them profitable compared to several other for instance European carriers).

They've done a quite lot for Schengen lounges in MUC, and new lounges will open in FRA when Pier A Plus opens next year.

Yes- MUC has improved certainly.
The Pier A Plus will be a huge improvement at FRA- I am sure someone will complain however that the FCT is gone

I am Silver with LH, but I end up flying KLM / AF several times per year because I need open-jaw tickets. I fly Berlin to, say, Rome, but want to come back from Bologna (economy). Now, if I try to buy such a ticket on www.lufthansa.de I have to try each option on the days I could be flying to end up seeing the price (which can change of several hundred Euros from flight to flight). So I end up booking on klm.de where they show me prices and conditions for all the flights of the different days right away. I wouldn't mind paying a bit more to fly LH (and enjoy the lounges / extra luggage allowance!) but I DO mind spending two hours trying to figure out the different options!

If they set up their website in a different way, boy, it's LH all the way!

Excellent point. I use a T.A. with LH as invariably they are able to figure out things that are very difficult on the website (like fly one direction with LH and return on LX on the same ticket).

I am a weekend traveler so mostly the lounge situation does not affect me that much (but yesterday in VIE).
Still LH/M&M should improve the lounge situation and create more space.
The free Internet part should be fixed asap as well but the reason appears to be a long-term contract with T-Mobile/Telekom which prevents Lufthansa from offering free service. LH better starts offering free Internet before everybody has UMTS with a data flat including roaming ;-)
I cannot use my eVouchers because I often travel in cheap Economy classes. I won't complain about being upgraded to the US or Japan from S or L class but would have happily spent eVouchers to know in advance that I'll be able to sleep in C. If there is a light load LH should allow eVoucher upgrades (at least Y->C) at check-in.
In Y I haven't been personally greeted by name since probably half a year (although every time in short or long haul C). This is a personal touch I kinda like. I rarely see the PIL on the drinks cart, though.

Overall I receive OK service but the experience could be better.

Fully flat C beds
Improved Y on longhaul (the leg space and lack of entertainment is from last century)
Stop screwing around with M&M, leave it working the way it is

There should be fewer restrictions on eVouchers than upgrading with miles.
Having said that it's one of the most annoying facts of the upgrade section M&M website. This type of information (which booking classes are allowed to upgrade) is not transparent

GBM