Can someone sanity check me?

Booked (but may change...keeping my eye out for options)

LGW-LIS-ZRH-IAD-CLE as a one-way award ticket. (CLE-EWR-LHR as a much simpler separate award)

LGW-LIS is operated by Portugilia with a TP flight number in "I" class
LIS-ZRH is operated by Swiss with a LX flight number in "I" class
ZRH-IAD-CLE is operated by UA with UA flight numbers in IN and XN class.

None of the stops are long enough to meet the definition of a stopover, so I expect if I check a bag it will be checked a LIS through to CLE with normal re-check formalities in IAD.

United is quoting a first bag fee (limit 50 pounds/23kg) of $195 or €180 depending on where I look, seemingly making no allowance for being a Business class fare or *G status.

When I pull the PNR on TAP's website it appears to imply 70# (though quantity is unclear).

Is it reasonable for me to expect that I'll be able to check 1 bag (probably in the 30# range) free or should I trust UA's baggage fee disclosure for once?