Citation V/Ultra/Encore (C560)
Situational Awareness
Conflict NMAC; Deviation / Discrepancy - Procedural Published Material / Policy
Flight Crew Became Reoriented; Flight Crew Took Evasive Action
Human Factors
Takeoff was from LOT runway 20. Winds were 200@12. From what we could tell; everyone at this uncontrolled airport was using 20. During taxi out and during the takeoff briefing; flight crew discussed it was a beautiful Sunday afternoon and everyone was out flying.  We discussed keeping our eyes open for VFR traffic. I tried to get our IFR clearance over the radio several times during taxi out but found that we were unable to hear ATC and they were unable to hear us. I was only able to hear other aircraft talking to Chicago Approach. We elected to get our IFR clearance in the air.Before boarding we heard the FBO line staff expecting two Challengers inbound pretty soon and were eager to get rid of us. Listening on Unicom; we heard a few small aircraft in the pattern and at least one of the Challengers several miles to the South intending to enter downwind for 20. A C172 taxied out ahead of us and departed just before us. At least one other GA aircraft was taxiing on the field; and one other on downwind for 20.  With Base and Final clear I announced our departure and intended south course away from the airport. Taking the runway; I remarked we could not see the ends of the other runways. We heard no other announcements from any other aircraft; and never heard anyone using a runway other than 20. After lifting off the runway; and about time for my required 400 feet call; I noticed an amber traffic covering our airplane symbol on the TCAS display (Range was set to the lowest which is 6nm). The number '300' showed next to it; and at first I could not see the preceding symbol '+;' or '-.' (Our own aircraft symbol was preventing view of the '+'). I assumed the aircraft must be on the ground below us but I was alarmed to finally determine it was a '+.' I realized the other craft should be right on top of us. When I leaned forward to look up; the corresponding movement of my side post (in the right seat; the side post covers the 1:30 line of sight) revealed an aircraft that had been hiding behind it converging with us both horizontally and vertically.  I announced; 'Traffic!' The Pilot Flying (PF) lowered the nose and caught sight of the C-172 and began a left turn. It at first appeared this would reduce our closure rate and give both of us (aircraft) the time to best figure out how to miss each other. But the other craft began a gentle left turn which canceled out our initial left turn leaving the closure rate not much changed. Alarmed; I grabbed the controls and increased the bank and added a slight nose down. I felt the other aircraft appeared to see us; and elected to turn left to pass behind us; but their turn was shallow and gentle; not aggressive enough to ensure adequate separation. Knowing I would have to give up sight of the other aircraft once the leading edge of our right wing covered it up; I wanted to be sure separation was assured no matter what he/she did after my line of sight was lost. I did see the other aircraft begin to increase its bank angle right as he passed out of view. This gave maybe 500 feet or less of separation.I let go of the controls; after having them for 3 or 4 seconds. We established the PF had the controls. I; embarrassed; apologized for grabbing the controls; and without any callout for it. The PF seemed OK with it; he understood the reason for it.  We tried very hard not to discuss it until out of sterile cockpit. We became very busy with Chicago Departure and less than a minute later had a Traffic Alert (TA) with another aircraft in the area.I looked down and saw I never did get the flaps up and retracted them.  I did call on Unicom that we were departing the airspace and were glad to have missed the C-172. I think I asked if they'd seen us but no one responded on the frequency. The rest of the flight was uneventful.One thing that would have been helpful; is to look at the TCAS lined up on the runway. This would have given us an idea before the takeoff roll of the aircraft'spresence. We could have had the opportunity to devise another avoidance plan.  I saw the TCAS before we took the runway; but the way the display is; at right angle to the runway; I could not see very well in that direction.  Taking the runway; I was busy with other duties and callouts; and didn't look at the TCAS until we were airborne. Secondly; going to unfamiliar; uncontrolled airports; in a jet; on nice weekend days increases the risk of near misses with VFR local traffic. Many times; the customer needs to go there at that time. But if there are occasions when we could go to the towered airport; we should seek those out.
CE-560 pilot reported an NMAC with a high wing light aircraft while departing LOT airport.