No, what happens to make me believe it is the fact if Lena rejects his advances which he initiates afterwards he doesn't put the word in for her like he said he would. His demand is carried through his actions and the consequences, not his words.
"I'll do you a favor" followed by getting handsy has clear implications to any adult who's worked with shit bosses. Why are we even pretending to be clueless about the nature of the deal here?
How else was he supposed to ask her out? Maybe
without making it a condition to tell her what he claimed was important information regarding her work? I'm acting like it was a sleazy piece of blackmail, because it was.
You are now inventing something that's not there (or reverting the timeline) It's not a matter of choosing between Lena and another woman when Lena and Robert spoke. Lena's contract was supposed to be reduced/cut due to the mess caused by Axel:
Python:
r "It seems Samantha overheard the chef and the staff chief talking the other day."
l "About what?"
r "About you."
l "About me? Why?"
r "Well, Friday's incident made quite a ruckus. People are talking about it..."
l "Oh, God..."
r "And the chief wasn't too thrilled about what happened on Thursday's service when they had to send you home early."
l "But that wasn't my fault! None of it was..."
r "Of course not, but I guess they're not too pleased with your personal life interfering with work..."
At no point it is claimed that it's supposed to be some sort of a choice between two workers. The "other worker" only pops up later as excuse why Lena had to be let go.
Also, as for why he should put the word in for Lena instead of the other worker -- maybe simply on professional level, because Lena is the best waitress they have, according to Robert himself?
Lena ultimately working at the restaurant, has nothing to do with Robert. Seymour decides he doesn't want her working there, after their meeting in Chapter 3. And it's after that, that her hours are reduced. Plus Seymour is actually having a meeting with Axel, when the first incident occurs, because we actually see him stood right next to Axel, before him and Lena start arguing. Isn't it just as likely that Seymour is behind it all from the beginning? Robert is just relaying something someone else overheard. So we don't know for certain who is really behind it, we're relying on some gossip that Robert has been told about.
Even if Lena knows Robert did put in a word for her, she still has her hours reduced. That's almost certainly Seymour trying to get her to leave. When she doesn't, he expresses his surprise that she's still there, and shortly after that she gets sacked. Robert even says at the time, he can't understand why they're reducing staff numbers, because they're short-staffed as it is. The clear implication, is that it's Seymour attempting to persuade Lena to go. But he wants her to choose to go, so that she can ultimately become reliant on the income he provides.
You say Robert doesn't put in a word for Lena, if they don't have sex. But how do you know that's the case, instead of Seymour overruling him, and deciding to get rid of Lena early? That could just as easily have happened, because Lena just assumes he didn't, being totally unaware at that point, that Seymour is actively trying to sabotage her earnings.
The scene you mention above has no relation to her contract being cut, that comes later, after Lena's meeting at the restaurant with Seymour, in Chapter 3. During the meeting, Seymour expresses surprise, that a girl like her is working as a mere waitress. The implication is, she should leave if she wants to be his model. From that moment on, it's Seymour and nobody else who is trying to get her out of the restaurant. Regardless of whether Robert puts in a word for her, she has no chance of keeping that job. And since nothing is related, beyond Lena's supposition, it's impossible to know either way.
You also say her going out with him, was a condition of him telling her important information about work, and that is your basis for him blackmailing her. Well since he didn't bring it up, till they were already on their date, that's obviously not the case is it? She goes out drinking with him to Shine, because she feels she owes him, for standing up for her, when Axel confronted them on the street. And Robert got beaten up. It has absolutely nothing to do, with anything remotely sleazy, as you seem to believe.
If she doesn't offer to take him out for drinks, which is pretty inconsiderate considering he got beaten up, trying to protect her. Then he brings up about the important information he needs to tell. But him saying, work is not the appropriate place to tell her, is completely reasonable, bearing in mind it's information he isn't supposed to know about. It's safe to assume the staff chief and the chef did not intend any of the other staff to hear their conversation. Robert is just being cautious by wanting to tell Lena outside the workplace. There's no reason to suspect as he has some devious motive, as you try to make out.
I think you're making a mountain out of a molehill. Robert doesn't try to blackmail her. She either offers herself to take him out for drinks, because she wants to repay him for standing up to Axel. In which case, Robert only brings up the important information, after they've been chatting and flirting for a while. If Lena asks him out for drinks herself, it makes no sense that she would respond negatively to him, if he didn't give her any cause. Which means at the very least they would have had an amicable evening. And therefore it's not beyond the realms of possibility, to assume that Robert believed that the 'date' was going well, and that he was justified in believing that Lena might respond positively to an attempted kiss. If he got it wrong, well he wouldn't be the first guy to do that. It doesn't make him a bastard, it just makes him mistaken. Nothing more.
And if it goes the other way. Well a case could be made, that Lena isn't behaving very well, by taking Robert for granted. He risked getting seriously injured, and might expect at least some gratitude from her. Even if she doesn't like Robert, and she gives no indication prior to this, that that's the case, you would still expect her to make some kind of gesture as recompense. And if she doesn't, she's being pretty ignorant. So personally, the choice where she doesn't offer to go out for drinks, makes no sense whatsoever. From my perspective, that has to happen, because that's what Lena would do. So she does go out for drinks with him, and the other choice where she doesn't is irrelevant, because the real Lena would never do that