I've mapped mouse-RNA-Seq data to a genome using the Gencode M17 comprehensive annotation .gtf file. Then I did read-counting using featureCounts, but I supplied a subset of the annotation, containing only lncRNA annotations. This leads to  only 1-2% of all reads to align successfully (usually less than 1 Million total reads of a library). I think this is to be expected given the relatively low expression levels of lncRNA genes.

Now this really affects the AveLogCPM values and the low-count filtering using the cpm() function of edgeR.

Is this way of read counting using the lncRNA subset a valid approach (statistically speaking)? This really greatly affects p-values and logCPM.

How could I adjust low-expression filtering to accomodate this?

It seems like you're making life difficult for yourself.

Firstly, you should use the entire annotation during counting - this ensures that featureCounts will be able to detect and remove ambiguous read assignments. For example, if a lncRNA overlaps with a protein-coding gene on the same strand, you cannot distinguish reads from the two transcripts - featureCounts will recognise this and avoid assigning any reads in the overlapping (exonic) regions. However, if you only provide the function with a subset of the annotation, all reads in the overlapping regions will be incorrectly assigned to the lncRNA even if they originated from the protein-coding gene.

Once you do that, most of your problems with the interpretation of the CPM will go away. You can filter on the CPM as described in the user's guide, and if you so desire, further filter on genes annotated as lncRNAs. The resulting count matrix can then be used in the rest of the edgeR pipeline. (I should add that, if you were using filterByExpr, the high-abundance filter should not be greatly affected by prior subsetting for lncRNAs. This is because the filter threshold is chosen at a CPM corresponding to a pre-specified absolute count; if you subset by feature, the CPM threshold will naturally adjust itself to preserve the threshold on the absolute count. And obviously, for retained genes, the actual counts in the matrix do not change upon subsetting.)

The real issue is how you decide to normalize. If you use only the lncRNA counts in calcNormFactors, you are assuming that most lncRNAs are not DE across your conditions. If you use all (high-abundance) counts in calcNormFactors, you avoid this assumption, but you then make a different assumption that scaling biases for lncRNAs are the same as those in the rest of the transcriptome. The choice between these two strategies can potentially have quite an effect on your DE analysis, e.g., if lncRNAs are globally upregulated in one condition. Personally, I would go for the second strategy; if I recall correctly, lncRNAs are not too different from protein-coding mRNAs in their biophysical properties, so it would be surprising to see different sequencing biases between the two classes.

If the sample-to-sample fold changes in the effective library sizes (product of the normalization factor and library size) are similar between the two strategies above, then there should not be a major difference in the p-values. The absolute scale of the normalization should not have a major effect on the calculation of the p-values, as that information is irrelevant when comparing across samples.