"Markeneke" might also be Margininkai, of which there are 4, in the following districts:
And the source for "Iddly" was?
It is always best to exhaust U.S. sources before trying the less accessible records in the Historical Archives of Lithuania. The trick is to identify the place of birth or at least where the immigrant lived in the Old Country. Without this information it is virtually impossible to find records there. Once you have that information, you can write an email to the Archives and request a translated copy of the person's baptismal (and therefore, birth) record, etc. So if I were you I'd try to get naturalization records, death certificates, church marriage records, etc. Family history may tell you if there were siblings to these folks and what their names were. A similar search for their records in the U.S. is often a good source of the necessary information. The records in the Archives of Lithuania are mostly not digitized and therefore not searchable by computer. The staff there or researchers there have to examine the original record books organized by parish name and by year, paging through them to find a given name. They are very good at it, but they do need more than what you have so far.
Death certificates are usually held by the state vital records department -- you'll probably have to do a bit of searching to find where these are stored. Sometimes they are held by the County Clerk of the county in which the person died. Church marriage records (not a marriage certificate proving that someone was married) are often fruitful sources of the required information and most Lithuanians married in the nearest Lithuanian church -- again a bit of searching will reveal what church and a phone call or mail to the diocese will tell where the sacramental records of a church now no long in existence are held.
If you post all the information you already have about them (including details of dates, names, etc.), some of us with subscriptions to ancestry.com will be able and willing to do some searching for you.