Millwall were bottom not so long ago but they are recovering and this completes three successive draws against QPR, Reading and the Clarets.
Lomas was pleased with the point with his only disappointment coming with what looks set to be a long term injury for Scott Malone.
"We're improving and we can take heart from the way that we have played against three good sides in QPR, Reading and Burnley this afternoon," he said.
"We've not got to focus on turning these draws into wins. If you can get two or three victories it can really push you up the table.
"We're a little disappointed with their second goal from a defensive point of view. We paid the price for not quite defending well enough. Before that we hoped to go into half time with the 2-0 lead but had a bit of misfortune with the goal they pulled back."
Dyche was realistic about Burnley's first half performance. "We didn't start well and you have to be realistic," he said. "Being 2-0 down is a tough scoreline to change, but we had to do it the hard way and I think there was again evidence that we have a good mentality in the group.
"Without taking anything away from Millwall, we weren't at the races for the first half an hour, but the second goal, which had an element of luck for them with the deflection, just seemed to kick us into life.
"We looked back to what we are all of a sudden and the break actually came a little bit too quickly for us. We were on the front foot but we responded again and took that into the second half when we created some good chances and probably deserved to edge it overall."
The closest we came was when Scott Arfield hit the post with Sam Vokes claiming a penalty in the immediate aftermath. "I felt it was a penalty," Dyche added. "I'll make it clear I thought the referee had a good game at a difficult place to come, but if that incident happens anywhere else on the pitch it's a free kick, so for me it's in the box and it's a penalty.
"Overall, I feel most people will feel we certainly deserved to get back into it, and I just thought we edged it. We knew this would be a firm challenge, but that's this division for you.
"We've had to earn the right to take a point, but you are going to have to do that, but a draw away from home is never a bad result and we're in good shape.
"We are there to be beaten because we are at the top, but what a great position to be in. I don't think many fancied us to be there, but that bodes well for what we are trying to achieve as a group as we move forward and we are proving a tough nut to crack."