There are two possible approaches to this task.
The first option would be setting custom linestyle as ByLevel symbology. If you use only one custom linestyle (+ as many standard styles as you need) per level, this will probably work for you. Although, the symbology of the element will always be shown as 'ByLevel' which is not the same as physically assigned symbology.
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The only thing you need to do in your workspace to use ByLevel symbology is to create igds_style_set_bylevel attribute using AttributeCreator and set it to 'yes'.
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Your seed-file should have all the levels and their symbology defined OR you can set the ByLevel style in your destination feature Properties > Parameters > Level Style.
The second option is actually a workaround, but it will also solve the problem.
-DGN v8 Reader reads custom linestyle name into igds_style_name attribute;
-however, DGN v8 Writer does not support igds_style_name (as well as igds_custom_linestyle) attribute currently;
-both - Reader and Writer - support igds_style attribute, which is MicroStation internal linestyle ID.
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In your workspace, create igds_style_name attribute using AttributeCreator or expose the attribute on the source feature type if your source format is DGN v8 and set it to a proper custom linestyle name for each feature;
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then map it to the corresponding igds_style number using AttributeValueMapper. To make sure that igds_style values are correct and avoid manual typing in, AttributeValueMapper can import igds_style_name/igds_style pairs from LinestyleLookUp.dgn - a dgn-file that contains every custom linestyle you are going to use. As you need to 'introduce' every custom linestyle to the seed-file anyway (see FME Readers and Writers > Bentley MicroStation Design Reader/Writer > Feature Representation > Custom Line Styles > Providing the Correct Seed File), you can:
-draw elements using different linestyles in your seed file;
-save a copy of the seed-file as LinestyleLookUp.dgn;
-delete all the elements from your seed-file.