Remember, this is an analysis from a non-attorney. Please use this answer at your own risk.
There are several rules that have been put in place in regards to an LPFM station's relationship to a full-service station. §73.858 prohibits an LPFM station from being held by a party who has attributable interests in other broadcast facilities or other mass media under Commission regulation (such as cross ownership of in-town newspapers), §73.860 outright prohibits LPFMs from holding interest in any other broadcast facility (with carve-outs for tribal entities, FM translators for the LPFM station and accredited educational institutions with a full-service station and a student operated LPFM), §73.860 also prohibits LPFM stations from entering into operating agreements, time brokerage agreements or management agreements with other full-service or LPFM stations and finally, §73.879 prohibits the rebroadcast of a full-service broadcast station on an LPFM.
With those rules in mind, let's look at question being asked.
Currently, an LPFM station can be carried on a non commonly-owned FM translator. There has never been an objection to this type of arrangement, especially in cases where the translator licensee is donating the airtime on the translator to the LPFM station. The same argument can be made for HD subchannels (which for this discussion, I may refer to as "HD2"). If the licensee of a full-service station, especially a non-commercial station wishes to rebroadcast an LPFM station, there is no regulation prohibiting it.
The only times that there would be an issue is if there is a formal agreement such as a lease where the LPFM is paying the full-service station to be on the HD2. This is a a legal gray area. When you look at the intentions of the original rules going back to 2000, these rules were put in place to prevent full-power influence in LPFM.
We have also decided to prohibit operating agreements in any form, including time brokerage agreements, local marketing and management agreements, and similar arrangements, between full power broadcasters and LPFM broadcasters, or between two more more low power licensees [...]. We are concerned that such agreements too readily could undermine the strict cross-ownership restriction adopted by allowing an ineligible entity to program or manage an LPFM station. (LPFM Report and Order, 15 FCC Rcd. 2205 (2000) at 30)
If the LPFM station is paying the full-service station to carry the LPFM's programming on HD2, it may be seen by some as a time brokerage or operating agreement but with an effect not anticipated in the mindset of the creation of the rules. The Audio Division further interprets their mindset on these rules in the Dublab decision:
§73.860(e) of the Rules states that no LPFM licensee may enter into an operating agreement of any time, including a time-brokerage or management agreement with either a full-power broadcast station or another LPFM station [...]. Such agreements are generally defined as a type of contract that involves a station's sale of blocks of airtime to a third-party broker, who then supplies the programming to fill the airtime and if a commercial station, sells commercial spot announcements to support the programming. (Machine Project, Letter, File No. BMPL-20170612ACF, et al. (MB, Sep. 28, 2018) at 10)
With that said, we could interpret this by stating that the rules would prohibit the LPFM station from purchasing time (leasing) the HD2 and such a prohibition would be in contrast to a translator since the rules do not prohibit any kind of an agreement with an FM translator. The second way to work around this would be is to send the HD2 a separate programming feed, even if it slightly varies off of the LPFM station. Again, these are "CYA" methods to prevent the perception of a prohibited time brokerage agreement. This issue becomes completely moot if there is no consideration in connection with the full-service carrying the LPFM station on the HD2 as there is no "brokerage" involved.
Also, if an LPFM station is paying to be carried on an HD2 and knowing how expensive this type of leasing can be, especially in some markets, it further drives the question of how the LPFM is getting that funding (i.e. are they running full-blown commercials?).
If an LPFM station is being carried on the HD2 of a noncommercial station, it is important to also recognize that since the LPFM is not the licensee of the noncommercial station carrying the HD2, any extended fundraising on the HD2, even for the LPFM station could be required to follow the Commission's Third Party Fundraising rules and any fundraising on the HD2 for a different non-profit organization would cut into the non-commercial station's 1% of airtime per year allowance. Also, even fi the noncommercial station would let you third-party fundraise on the HD2, in order for the LPFM organization to be able to be benefited, they must have an IRS 501(c)(3) non-profit charity status. There should not be an issue with running underwriting acknowledgements over the HD2 stream that originated at the LPFM if the non-commercial station would allow it. Just keep in mind though that any violations to the rules regarding the content of underwriting acknowledgements (i.e. full-blown commercials or something in between) would reflect on the full-service non-commercial station and could make them liable.
Therefore, our answer is, "yes, but however...." An LPFM program can be carried on a HD2, however, precautions must be put into place to prevent the violation of any of the rules that protects the localism of LPFM while using the medium of HD radio in a manner that is in the public interest. This safest way to do this is to run a different programming feed (even if the programming is 99% similar) to the HD.
