You're likely right that there are gaps in the data - it just means that no-one there has mapped the area - best thing would be to get an Android phone with cellmapper and go for a drive to generate the data, then some days later cellmapper will show it.
Some councils in the UK hold and make available publicly mast locations, I don't know if that's the case for Ireland.
I don't know what frequencies 3IE run on, but the B315 is a CAT4 device, so it cannot aggregate multiple bands. If 3IE use multiple bands and their local mast has them then they may benefit for upgrading their router to one that can aggregate bands that 3IE uses.
Do you know what their current metrics are for RSRP/RSRQ/SINR - those would be useful to know to be able to see if anything looks like it could be improved.
Edit: looks like 4G+ should be everywhere as-of April 2016.
Three Ireland, the country’s second largest mobile operator by subscribers, has unveiled plans to roll out 225Mbps ‘4G Plus’ services to 56% of the country by the end of April 2016.
www.commsupdate.com
Given that, I'd think providing they're close enough to a mast with good enough signal a different router that can aggregate the bands would give a speed improvement.
Edit 2: it seems they use 800 and 1800mhz. If your friend is already only on 800mhz then I would think it'd be unlikely they'd get 1800 to aggregate them. But if they are on 1800 then I would think there'd be a good chance of aggregating with 800 if they had a device that could