Lee is as concerned as any player - or fellow fan - about the club's situation - but insists that there is still so much realistic hope for what lies ahead.
And he is by no means alone in his thoughts as he looks to the FA Cup game coming up, as he explains:
"After the game on Wednesday the lads were saying if we could go on and win this, get into Europe, and finish fourth bottom, it won't be such a bad season will it?
"There is no point thinking you are going to lose otherwise there is no point turning up on Sunday.
"No matter who you are playing, that is what everyone's attitude is, and everyone thinks 'yeah, we are going to win this game.'
"You have got to go into every match believing you are going to win - otherwise it is just a waste of time."
He says that cup glory going hand in hand with survival is not unattainable, and adds:
"West Ham finished seventh last season and didn't qualify for Europe, but everyone said it was a good season; this season we could win the FA Cup, qualify for Europe, and finish fourth bottom, and that would be good.
"Everyone is not happy because we are not winning but you have to take the positives, and if you start thinking negatively, that is when things can get really bad, I think.
"It is no easy achievement to finish seventh as we did last season; everyone knows things aren't going well at the moment and that we are losing games - no one is happy about it.
"But we know we have got to keep working hard, trying and trying - and then it will come."
As Lee settles in with his new teammates he is seeing the fire of determination burning in his colleagues' eyes - none more so than the 'Prodigal son', Paolo Di Canio, who is back on these shores after rehab in Bologna.
"I have just met Paolo and I have seen how passionate he is when he plays; he is a nice bloke and I am looking forward to playing with him.
"The fans deserve his passion and it can only be a good thing him coming back.
"A lot of players here are West Ham fans like little Joe who loves the club as well - and there are good players coming back now, so hopefully we will go on and start winning games."
Lee has now played three times for the Hammers since his arrival from Leeds, and, laying out his thoughts on the relegation battle, he explains:
"I wouldn't say we are under the cosh; we have got the same teams around us and we still have to play those teams.
"Bolton are four points in front of us, and they are out of the drop zone; when we play them we have got to beat them.
"Two wins and you are flying and well out of it, with the confidence given a big boost.
"If we get a couple of wins, you watch, everyone's spirit will change, because it will take you up and up.
"I think we will be all right; we have got the players, we have got the firepower, and at the moment it is just keeping them out.
"We have got to keep working at it on the training field to prevent it happening on match day - that is all you can do, and it is up to us once we are out there.
"You can't just blame the back four because you start the defence from the front, but on Wednesday it was a couple of set plays that did it."
Looking back on those first three games in more detail, Lee says:
"That was my first game and I hadn't done too much training but we got back to 2-1 up, everyone was working hard, and it was just unlucky, one of those things."
Of Jenas' equalising goal, he says:
"He sliced his shot and it has just gone in the top corner; there is nothing you can do about things like that - except keep trying and working hard.
"I think he had one just before that that went high up in the stand, but this one went in and if he had caught it truly it would probably have gone straight to David James.
"But you need a bit of luck and that is obviously not with us at the moment."
At least he was playing for the fans amongst whom he counts himself - and his family as well.
"It was a good time and I thoroughly enjoyed it, but it was just disappointing they nicked a draw in the end," he says.
"My family were all there, which was good, but I would have preferred the three points.
"The fans were really supportive and I was amongst them once.
"My mates were in the Chicken Run but my family were up high somewhere!
"The support has been really good and I think that will help us stay up."
As for the controversial defeat by Arsenal, with that early dismissal of Steve Lomas, he says:
"It was, I think, a harsh sending off, and we had our backs to the wall with 10 men against Arsenal at Highbury - not good at all.
"The fight and the spirit was unbelievable - and so was the support, which was great, but it was just unlucky.
"The second goal just killed us and it should have been a foul as well, but the ref said 'ah, sorry, I have made a mistake' but that was too late, you know?
"They scored, we pushed on to try and get an equaliser, and they have nicked one at the end.
"But you can't fault the lads for their spirit at the moment; everyone is trying their hardest and it is just not happening.
"We could even have nicked the game against Arsenal; at 1-1 Trevor had a shot and it could have been 2-1.
"And just before half time I was in there all on my own when Jermain nearly got the ball to me - but it never happened, the 3-1 was obviously disappointing, but with 10 men after about 10 minutes it was always going to be a hard game."
Next up was a return to his first professional club, Charlton - and the chance to catch up with some old mates.
"There are a couple still there," he says, "and it was good to go back but again, it was a disappointing result to come away with nothing.
"It was a big game for us, our game in hand, and to let in four goals was really disappointing - but when it was 3-2 I thought we were going to come back into it.
"Trevor had a chance, and was unlucky because maybe he got pulled back a bit, then it was my fault for the fourth goal - I got caught on the edge of the box.
"I played with Michael on Wednesday and it was good; I drifted more in the middle and got some little passes with Michael.
"That is two local derbies that we have come away with nothing from.
"But it is in the past now and you have to keep thinking of the future - and the next game."
Lee was impressed with Wednesday evening's two debutants, Les Ferdinand, and Glen Johnson, and he adds:
"Les is going to be big here; he is strong and a good target man - he has got good experience and it is going to help us.
"Young 'Johno' came on against Charlton and I think he is a really good player; when he will start I don't know, but I would definitely give him a go, as he is a really good player with a good future."
As for the next league game against Blackburn next week, Lee's message is simple.
"We have got to be looking to win that game; no draws or losing, and everybody knows that," he insists.
"All we can do is go out there and try our hardest."
Which is something Lee himself could never be accused of not doing.