Looking over the notes a cousin had made in her research on a 19th century date of death, I saw a Hebrew date (Adar 18) and civil date (Feb 18). It is very unusual that the calendars are in sync like that.
So I went to a calendar converter and discovered that Adar 18 that year was March 1. February 18 was Adar 6. Either way, one of the two dates recorded was off by 12 days.
My cousin doesn't usually make mistakes like this, and she was quoting the Lithuanian Archives as her source. I looked at the archival database on JewishGen, and the records matched. So maybe someone else made the mistake in the transcription, and my cousin hadn't checked the dates like I had.
Further research indicated I was the one in error -- as I was using the wrong calendar converter.
The Gregorian Calendar, named after Pope Gregory XIII, was decreed in 1582 by the Catholic Church, and since then has become so widely used by Catholic and non-Catholic countries alike, many people probably think it is universal. Or at least, while one might be aware of other calendars like the Hebrew, Islamic, or Mayan calendars -- if one sees a date that looks Gregorian, we assume it is Gregorian. This can be a mistake.
The civil calendar in use in Lithuania has changed over time. The Polish-Lithuanian Commonwealth was an early adopter of the Gregorian Calendar in 1586. However, in 1800, when Lithuania was annexed by Russia, there was a return to the Julian calendar. The Russian revolution of 1917 reinstated the Gregorian Calendar. [Source (linked above): Wikipedia entry on Lithuanian Calendar]
A side effect of this history is that dates on Lithuanian documents, such as vital records, between 1800 and 1917 are likely on the Julian calendar.
Once you know what calendar you're dealing with, converting from Julian to Gregorian is easy. Depending upon what century the date occurs in, you add a specific number of days.
16th and 17th centuries - 10 days
18th century - 11 days
19th century - 12 days
20th and 21st century - 13 days
For those who like mathematical formulas:
For the Nth century, add [[3*N/4]] - 2 days (where [[ X ]] truncates the integer.)
The question I don't have the answer to is how to record it in my database. I lean towards using the Gregorian date, since other dates in the database are Gregorian; Indicating in the notes that the Julian date is what appeared on the document. I am already converting Hebrew dates I find on tombstones to the Gregorian date for my records, and this is really no different.