It's not wise to take the last flights of the night if one must be at the destination for an important business meeting the next morning.....and employers shouldn't try to play cheap on tickets in such circumstances, although the employer might have decided to "self insure" and pay sometimes for tickets that are thrown away as in this case in order to save lots of money on many of these risky "self connections" across separate tickets when they do work out.

OTOH, if MAD runway constructions is causing delays, switching to TAP and connecting through LIS might make the problem worse rather than better in that delays in these situations tend to get worse as the day goes on, so the OP rebooking to take a later flight to LIS (scheduled for a later departure than the IB operated MAD-LHR) and then doing a connection at LIS to a TAP flight LIS-HEL with no *A status doesn't seem like a proactive improvement to me. Yeah, TAP will rebook the LIS-HEL segment if the connection is missed as presumably it's all on one ticket, but this doesn't help the OP to get to HEL in time for that early morning meeting. In fact, I suspect that there's an earlier LHR-HEL flight than LIS-HEL if the outcome is that OP is stranded somewhere along the way.