Thanks for the support.
I guess that would be my next step
The fact that I have very vague starting points concerns me that I won't get very far.
With some luck, persistence, and ingenuity you might be very happy with what you're able to learn.
Here's what I would do if I were you. I'm assuming you are a subscriber to Ancestry.com. If not, do subscribe. (You really don't need the international version -- there's little or no info from Lithuania on Ancestry.)
1) Try to get actual copies of Martin and Mary's death certificates. (There will be a charge.) The one who died first (Mary) is probably the best, as it should contain information provided by the survivor. That might tell the city they were from. The city name could be unrecognizable, but it might at least give you the first few letters of the name and you can search from there.
2) Try to find their names on a passenger list. Jankauskas found that they arrived in 1905, and while that could be off by a year or two, it seems that people usually told the truth to the census-taker about the year they arrived. (But they often lied about their birth dates, especially as they got older!!) The passenger list might give the name of the city they're from. They almost certainly took the Hamburg to NYC route.
3) Try to find them on the 1910 census, because that's where they will have been most truthful about the years in which they were born. Compare what you find on the various censuses, to the death certificates. Probably the month and day of their birth will be correct on the death certificate, but again the year might be a fib.
4) Take a guess at the city they came from, using the info from the passenger list and the death certificates. I'd bet on Kėdáiniai, as I said in an earlier post. But if what you find doesn't look like it's even close to Kėdáiniai, look at the very bottom of this page under "Kaunas County": https://en.wikipedia.org/wiki/K%C4%97dainiai
and see if what you find looks a little like any of those places.
5) Armed with that info, contact the Lithuanian State Historical Archives http://www.archyvai.lt/en/archives/hist ... hives.html
, give them the names, dates, and places you found. Ask them to search records for individuals who might match your ancestors in the area you mention.
They should write back and they should either give you a quote for the search, or they should let you know what they found and what they will charge you to provide the records. I expect the search will cost $100-200.