Lyria is the name of a joint venture of the Swiss federal railroads SBB CFF FFS and of the French state railways SNCF. Lyria takes care of fast "bullet train" traffic between Switzerland and France. Lyria uses Swiss staff on the SWiss side of the border and French personnel in France, but all the trains are maintained by the French SNCF. SBB owns two of the trains and SNCF owns seven. Technically Lyria is nowadays a company of its own under French law. The key routes which Lyria serves are Paris-Genève and Paris-Strassburg-Basel-Zürich. During ski season times some of the train routes are extended to Interlaken and Brig. Other routes of Lyria include Genève - Marseille, Lausanne-Paris and Bern-Basel-Paris.

This TGV train is of the new generation TGV POS 2N2. Painted and taped in the new Lyria livery, it runs now in the traffic between Genève and Paris.
Picture from Genève Cornavin 9.2.2020 by Ilkka Siissalo.

The same TGV train as shown above. Note how it shows both the logos of SBB and of SNCF at its side.
Picture from Genève Cornavin 9.2.2020 by Ilkka Siissalo.

The same TGV Lyria train as shown above, but seen from its other end.
Picture from Genève Cornavin 9.2.2020 by Ilkka Siissalo.

A TGV Lyria train on its way from Bern towards Basel and Paris. The picture is from 2016 and in those days it was still common that the Lyria services were run with these older TGV Sud-Est trains, but in 2020 practically all Lyria services are run by doubledecker TGV POS trains.
Picture from Olten 6.5.2016 by Ilkka Siissalo.

A Lyria TGV Sud-Est train is just leaving the Paris Gare de Lyon station towards Genève.
Picture from Paris Gare de Lyon 19.10.2017 by Ilkka Siissalo.

Similar to the one shown above, another TGV Sud-Est train no.4415 is boarding passengers bound for Switzerland a couple of hours later than the picture above.
Picture from Paris Gare de Lyon 19.10.2017 by Ilkka Siissalo.

TGV Sud-Est train no.4411 waiting for its departure time towards Basel and Paris.
Picture from Zürich main station 1.10.2015 by Ilkka Siissalo.

Swiss SBB and French SNCF had a long history of cooperation in TGV traffic already long before the joint venture Lyria was established. Already in the early 1980s SNCF changed some of its TGV trains to be able to run on three different voltage systems, one of them being the Swiss/German 15 kV AC. Already then SBB bought two TGV trains which SNCF maintained - just like the present day Lyria trains. The first SBB owned TGV trains were orange, similar to the early French TGV livery. They were of the type TGV-PSE (Paris-Sud-Est). This is one of the TGV-PSE trains in Zürich in 2003. It had already been painted in the new grey and blue colours and was no more orange. This train no. 117 was owned by the French SNCF, but as mentioned, SBB owned two similar trains.
Picture from Zürich main station 2.12.2003 by Ilkka Siissalo.

The same TGV-PSE train as above. The name Lyria was not yet invented in 2003, but SNCF and SBB used a heart-shaped logo and a marketing name "La Ligne du coeur France Suisse" (The line of heart France-Switzerland). This train unit no.117 was built in 1985.
Picture from Zürich main station 2.12.2003 by Ilkka Siissalo.

A TGV train owned by the Swiss SBB. Note the large SBB logo by the side of the locomotive. This is a TGV-Sud-Est unit. This train consisted of two TGV units. It had here just arrived from Paris to Basel. Here the two units were split. One part continued to Zürich and the other part via Olten to Bern.
Picture from Basel SBB station 16.7.2007 by Ilkka Siissalo.

The same train as shown above. The TGV unit which fills most of the picture is un it 4406 owned by SBB and the other unit (head of it barely visible at the bottom of the picture) was a similar TGV-PSE no.4408 owned by the French SNCF.
Picture from Basel SBB station 16.7.2007 by Ilkka Siissalo.