Depends on the lie and the timing of it, but all government agents are allowed to lie. That is, what you describe doesn't associate just with the feds. Your state and local agents have exactly the same tools at their disposal.
” Your state and local agents have exactly the same tools [lies] at their disposal.”
Absolutely. If I am ever part of an investigation I would be the biggest prick: “So, you say that, but isn’t it part of you job to be a liar?”
“Since you are allowed to lie to me I have nothing to say to you. Show me your warrant or get off my property. Take it up with my lawyer.”