My first questions would be who do you flight most often with and what are your "natural" choices? If you are mostly a US/NA flier (UA/US/CO maybe AC if you fly within or to/from Canada often) with a couple of TransPac/TATL flights per year and mostly in paid Y (ignore upgrades), LH doesn't make that much sense as any NA carrier will only recognize you as a *G - below GS/1K and 1P or whatever US/CO/AC's equivalent happens to be.

But if you fly heavily within europe or to/from Europe in business or first, then LH starts making more sense. You can make *G more easily (100% bonus for business with generous "short hop" min. business miles vs 50% for UA w/o any min miles- even higher for TATL F), you get upgrades, etc... The extra miles and status can overcome the extra taxes/fees. So my main suggestion is look at your "normal" flying pattern and let that decide what your "home" program should or could be. If you are just looking for *G status as a "second" home (flying oneworld or skyteam mostly), then the equation changes yet again. OZ/TK/AC are general preferences due to relatively low status mileage requirements.

Enjoy - and I'll really envy you if you can fly paid TATL F

As a further note to correct khyung- *G status from anyone outside of UA/US/CO entitles you to lounge access on all routes as long as a *G lounge exists at that airport. Domestic, int'l, etc... So a SEA-SFO routing gets you access to the RCC (yippee !!!) with AC/LH/SQ etc... *G card. It is only the American airlines that limit their own (or other American carriers) *G members lounge access to int'l routings.