It depends on what you consider as “syndicated” programming.
While there are some who feel that LPFM should be strictly about “local” programming, there are many justifications where “importing” programming from non-local sources can help meet local community needs. This includes programming that touches on national and international current events, educational programming, cultural programming and for minority expat communities, a “link to home”.
Keeping it noncommercial
Care must be taken to assure that programming that is carried is “non-comm friendly”. You must avoid programming offered by commercial programming sources unless you take the time to remove all commercial announcements and all references to commercial sponsors (which can be sometimes embedded in the programming and not in delineated commercial breaks). Carrying commercial syndicated programming may not be an option without paying a much higher rate to the program producer. Most LPFM stations don’t have that level of funding. Since commercials are prohibited on NCE (LPFM) stations, it would not be practical to have a “barter” agreement (carrying the national commercials in exchange for carrying the program).
The ban on commercials does extend to any programming not produced by the station
§399b(a)(1) of the Communications Act defines an "advertisement" as "any message or other programming material which is broadcast or otherwise transmitted in exchange for any remuneration, and which is intended- to promote any service, facility, or product offering by any person who is engaged in such offering for profit.".
This section also prohibits time brokerage (which we will discuss in a bit) and paid political messages or time blocks.
Remuneration is something given for something in return. In most contemporary cases, we see this term used in labor law in respect to employee compensation that is both monetary and otherwise (such as benefit plans). Remuneration can be more than just cash. It can also include the provision of the program.
Further, §399b(b)(2) states that no public broadcast station (which is defined elsewhere as any noncommercial educational broadcaster, which LPFM falls under) may "make its facilities available to any person for the broadcasting of any advertisement".
It can be easily interpreted that the reach of this law is to also include syndicated programming as well as locally produced programming. By carrying the syndicated programming, the licensee has made "its facilities available" to the outside program producer. If the syndicated program has any material which the program producer received remuneration for (even though the licensee received no benefit), it is still considered an "advertisement" under §399b(a)(1) and thus prohibited.
Avoid time brokerage opportunities
Likewise, you need to be careful with programming or network offerings where the station will be paid for carrying a program. For example, Immaculate Heart Radio (IHR) offers the Catholic network Relevant Radio to NCE stations. In return, depending on how much airtime is devoted to the network on a local station, the network will compensate the station based on a portion of “pledge drive” revenue. While this is legal for full-service NCE stations, it may not be for LPFM stations. This is due to a rule (§73.860(e)), that is unique to LPFM, that LPFM stations are unable to enter into any kind of an operating agreement, time brokerage or management agreement with a full-service broadcast station. IHR (now operating as Relevant Radio, Inc.) is the licensee of dozens of full-service broadcast stations across the country. For Catholic programming, EWTN may be a safer alternative.
This does not just apply to radio networks that are carried for a good part, if not all of the broadcast day. NCE stations cannot receive remuneration for any programming material which is intended "to express the views of any person with respect to any matter of public importance or interest" (47 USC §399b(a)(2)). This means that NCE/LPFM stations cannot sell blocks of time (whether it's 30 seconds or a few hours). Underwriting acknowledgement is strictly a "mention on the air" but cannot be sold in blocks the same way traditional commercial advertising is.
Free programming is out there
With that, many LPFM stations are carrying national syndicated programming. Programming like “Democracy Now!” is available free for all noncommercial stations. Additional free block programming is available directly from program producers and from aggregation sites like Radio4All.net. Some program producers also offer their programming free to LPFMs. In many cases, they just want to hear their voices in other cities. A good resource is the Radio Program Syndication, Imaging and Voice Overs group on Facebook.
Pacifica Network is your best option
Several dozen LPFM stations are affiliated with Pacifica Network. Pacifica operates AudioPort, which includes a large assortment of talk and music programs that are available for affiliates to use throughout the day. These programs are non-comm safe. For LPFM stations, an annual Pacifica membership runs about $500/year, but with the vast assortment of programming available, it can be worth it.
Local programming pledges and syndicated programming
A small number of LPFM stations that, during the 2013 filing window, directly used their preference points to eliminate other applicants are obligated by their pledges to carry a minimum of 8 hours of local programming per day. A list of those stations can be found on the Pledge List at REC. Even for stations on that list, it does not stop what they do in the other 16 hours of the day (within all of the other rules, of course). For LPFM stations not on that list, you have no specific restriction on carrying nonlocal programming, even though the station made a specific pledge on their application to do so, the station did not need to use that pledge in order to gain the station and therefore, they are under no obligation.