If you have used adapters containing barcode sequences (that identify
each patient), you would presumably end up with one single tube with
your libraries in it right?
Only if you pooled the individual libraries into one pool/tube.
If so, you then "put" the contents of that tube along with DNA
polymerase and nucleotides into one single lane of a flow cell? Your
provider would then give you raw FASTQ files that have been identified
using this barcode? So you would effectively received one (or 2,
depending if it's single/paired-end sequencing) FASTQ file per patient
You should get one (or two for PE) files per sample (patient) after demultiplexing. If you receive the data non-demultiplexed then one (or two for PE) files (for entire data) will contain all samples. You will need to separate them yourself.
If you do not use adapters with barcodes, does that mean you would
have to use a sequencing lane per patient? If so, that would vastly
increase the price you pay your provider, would it not?