Brussels/London/Paris to Lille, France

Thank you for your help, Roe. That's just what I needed to know.

In case you do any more investigation, be aware that there are two international train stations in Lille. But they are almost adjacent, and both have Metro stations and taxi lines. (The two Metro stations are on different Metro lines.) It can be over 500m on foot to change worst-case trains between the two stations, but you're not doing that.

London Heathrow, I assume, but the other 3 would have the same problems, none are directly connected to the continental rail system. You would have to transfer stations and trains in central London in order to catch the Eurostar from St Pancras to Lille. Paris flying in to CDG, there is indeed a TGV station at the airport. There are, according to DB, frequent TGV trains direct to Lille (about a 53 minute trip). This would be quite easy.
Brussels The airport is directly linked by train to Central Station, where you would change to a train for Brussels-Midi Station and in turn change for a train to Lille. Of the three choices, I think Paris-CDG is the easiest, Brussels the next, and London last, but all are possible if there is a very large difference in airfare.

Of course London is a city with a number of airports, not just Heathrow. Stansted, Luton, and Heathrow all have direct train connections to central London. London City has DLR trains to the door. Gatwick has direct trains into London, and has direct trains to St Pancras where, just by going up escalators, there is direct access to Europe via Eurostar.

I would agree with Roe that Paris seems the most straight forward. However, I think I would reverse 2 and 3. The Piccadilly line from Heathrow takes you to Kings Cross station which is connected via walkways to St. Pancras. Central and Midi stations in Brussels are a ways apart and would require changing trains. I recall having a bit of difficulty finding trains and buses in the Brussels stations.

Since I spent a day in London last year, and then went to Belgium on Eurostar, I feel entitled to confirm the original order: Paris, Brussels, London. I've also been in Brussels Central and Midi many times. The point is that at CDG and BRU, you roll your luggage a short distance from the baggage carousels to an elevator that goes straight down to the train platforms. Not only are the rolling distances in London hundreds of meters longer, you are almost certain to get stuck at the London-end with (at best) some escalators. St. Pancras is beautiful but also vast. I note that the OP didn't mention cost, perhaps because the new employer is subsidizing or covering the travel. That's important because the most expensive trains are going to have the largest luggage compartments at the end of the car (as opposed to tiny racks over the seats.) Imperial Class Thalys is clearly the way to go, CDG-Lille.

I would choose BRU. BRU would be my first choice. The airport is quite manageable. I've flown into Brussels a number of time and have always zipped through immigration. The airport is connected to the train station where you can easily make your way to Brussels Midi (aka Brussels Zuid). The train will take about 20 minutes. Most of the trains from the airport stop at all 3 Brussels stations so it is not necessary to transfer at Centraal as someone suggested. From Brussels Midi, you can get a TGV to Lille Europe that takes just 35 minutes. CDG would be my second choice for this trip, but it is a distant second for me assuming you have decent flight options to BRU. CDG is the European airport that I hate the most. Once you get through the airport and to the train station, it would be quite easy though to get to Lille and this could be a better option timing wise. LHR and LGW would be the longest journey. From either, you would have to make your way to St Pancras to catch the Eurostar to Lille. Unless you want to stay in London for a couple of days before continuing on to Lille, this is not the best option.

A small correction to Tim's post. Trains from CDG to Lille are TGVs, not Thalys trains.