The Free Software Foundation considers EPL and GPL to be incompatible. Based on my reading of their reasoning, it would seem that the LGPL would be similarly affected -- IANAL, please correct me if that reading is incorrect. Now, there is a guide for the copyright holder of the GPL-ed code to provide exceptions allowing for the code to be linked against incompatible libraries, but it'd still preclude linking to GPL-ed code from others (if the code is already linked against an EPL library), and the situation with linking a GPL-ed program against an EPL and another LGPL library seems unclear.
I'd like to know the answer to several questions:
The above diagram shows the relationships between licenses. Though not comprehensive, if there is an arrow then it is compatible.
From the Eclipse website it states:
The EPL and the GPL are not compatible in any combination where the result would be considered either: (a) a "derivative work" (which Eclipse interprets consistent with the definition of that term in the U.S. Copyright Act ) or (b) a work "based on" the GPL code, as that phrase is used in the GPLv2, GPLv3 or the GPL FAQ as applicable. Further, you may not combine EPL and GPL code in any scenario where source code under those licenses are both the same source code module.
Based upon the position of the Free Software Foundation, you may not combine EPL and GPL code in any scenario where linking exists between code made available under those licenses. The above applies to both GPL version 2 and GPL version 3.
In my opinion, unless an exception is made - LGPL and EPL code should not be combined. In fact, a lot of software is dual-licensed under LGPL and EPL.