I just tasted wedding cake at Hansen's(they have several locations but all cakes are baked at the Fairfax bakery). The cakes are beautiful...they do anything and everything that looks traditional. The buttercream frosting definitely has shortening in it because it has that body and stiffness that you're talking about. They have a ton of flavor combos and the designs are awesome.It definitely tastes like "old-school" cake. Good luck!
I used Cake and Art in West Hollywood on Santa Monica Blvd. just West of La Cienega. The cakes are truly beautiful and he only has 4 or 5 varieties. I'm not sure if the frosting was lard or butter but I know that it tasted delicious. It was also quite reasonably priced.
Sweet Baby Jane (on Beverly Blvd. or maybe Melrose in West Hollywood) is also pretty amazing but most of their frostings are quite light and fluffy. I haven't had all their cakes but I've had quite a few.
The most AMAZING baker is Joyce Maynor at Fantasy Frostings - I don't know about the lard-free factor, but she makes the most delicious cake. We having her do our wedding and compared to other companies, she is the best. Reach her at: 562.941.6266. She's in Whittier. Good luck!
Yes, Fantasy Frostings is supposed to be totally amazing, and the best cakes in L.A. from everyone I know that's tried them.
My wedding cake was from the Cake Collection in West L.A. on Berry, just south of Olympic. It was beautiful and delicious! The cake itself was super moist and the frosting was smooth and rich without being overly sweet. I did one cake with their amazing lightly tangy lemon and one cake that was chocolate-choclate chip with fresh raspberry puree - yum! It was a huge hit, and I was happy since my priority was a good tasting cake, not just a good looking one.
This probably doesn't help with your search for a Mexican bakery, however!
p.s. My second favorite cake is from Phoenix Bakery in Chinatown with fresh strawberries and whipped cream filling - mmm!