The former St Johnstone boss has replaced Kenny Jackett, who resigned at the end of last season after five and a half years with the club.
And Lomas says the Championship side's home form is the first thing he will be looking to improve.
Lomas said: "One of the areas from last season that we need to improve this year is the home form. I came here as a player and it was tough; that's how it should be for the opposition.
"They should be coming here knowing that it's going to be very tough to get anything.
"Why Millwall? It's a working class club with passionate fans. As soon as I knew there was an opportunity it's something I wanted to grab.
"It's a great league and an exciting league. Last season there was only 14 points between the top and bottom. It's a great challenge.
"At any club I've been I wasn't the greatest of players, but I was committed, determined and demanded effort.
"I did not like losing as a player and I still don't now. I can assure Millwall fans that I will give everything to make sure that we win.
"George Graham at Arsenal, Sam Allardyce at West Ham, Sir Matt Busby at Manchester United - there's a history of managers taking on clubs that are seen as rivals.
"I'm no different in that respect but I have a job to do here and am fully committed to doing it well."