I'm new to cake baking and designing. Wondering if you all have any ideas on what icings compliment certain flavors of cakes. Most of my customers enjoy a lemon cake with buttercream icing, which is great, but the combo gets kind of old after a while. I need ideas on icings that compliment cake flavors but pipe-able and decorate-able also.

You will get many different ideas as everyone's taste buds are different :)

Any b'cream can be changed by changing the flavoring used in it.  Try reading some of the recipes posted on this site.  Change the flavorings to match or contrast with the cake flavor.  There are no special icings that go especially with certain cake flavors.  Many people like Swiss Meringue or Italian Meringue b'creams - I don't as to me it's like eating a stick of butter straight out of the frig:( ; some like non-dairy whipped creams such as Rich's Bettercreme or Frostin Pride; other like me much prefer something like this one:  http://cakecentral.com/a/2-icing

You will probably have to try several before you settle on what is the perfect one for you and your family.

AThank you :)

APersonally, I like lemon cake with a tart raspberry filling & buttercream.

Lime filling also makes a nice change from plain buttercream.  So does white chocolate (try it as a ganache filling).

I use the Boyajian oils and flavours that are widely available across North America, for true natural fruit flavours.  You add them directly to buttercream made with less vanilla. Their raspberry is extraordinary.

And this may be personal taste, but a lemon cake with lemon icing and a drizzle of unsweetened (or bittersweet)  chocolate on top of each layer of the filling is a very unusual but excellent flavour combination.

There's cream cheese icing too, I like adding white chocolate to that.