The issue seems to be with the CUPS server related. CUPS for Linux lacks the clear manual how to use web-based administration tool to manage printers and jobs on server. Before reconfiguring CUPS I had only one entry on the CUPS printers page http://localhost:631/printers
HLL2400DW HLL2400DW Brother HL-L2400DW for CUPS
Logically, this is quite correct, as I have only one printer, and I used the Brother manufacturer's manual how to set up the printer. Connection: lpd://local_IP/BINARY_P1 However, it turns out that this is not enough for CUPS.
The solution was to go to the CUPS admin UI (http://localhost:631/admin), then add the printer using the first option for a network printer CUPS itself detected.
"Add Printer" > "Discovered Network Printers" > choose the first option
Now CUPS Printer page shows two printers:
Brother_HL-L2400DW Brother HL-L2400DW Home Lab Printer - IPP Everywhere
HLL2400DW HLL2400DW Brother HL-L2400DW for CUPS
but in LO Writer "Print" menu now I have 5 printers under different (!) names. And every time when I need to print I have to choose the correct printer (driver) from list. So all this just adds the confusion.
Edit: So I continued my research and I think, I finally found a solution. Problem is that printer have two drivers: one is "Brother installed driver for CUPS" that use lpd connection, and second driver is "Printer - IPP Everywhere" that use dnssd connection. The dnssd is a newer standard and is preferable - that's why I chose it as my default printer.The default printer selection is done through the Linux system dialog. In Debian:
System > Print Settings-localhost > Unlock > select default printer[Properties > Set As Default (one with dnssd)]. Then Lock settings again. Other printer driver should be disabled in CUPS web interface (Maintenance > Pause Printer)
Now it's OK,there are no delay before printing starts via wifi.
EDIT: Unfortunately, the issue is still present and appears from time to time.
