HI, does California CCP Section 339, "Statute ofLimitations" on a lease apply, if you have a written lease, but it states"verbally modified", in it, and the lease is breached, the landlord tries to sue 3.7 years later on it, although it states "verbally modified". Well past the 2 year statute on an oral contract. Thank you.

No what applies is this section:

337.2. Where a lease of real property is in writing, no action
shall be brought under Section 1951.2 of the Civil Code more than
four years after the breach of the lease and abandonment of the
property, or more than four years after the termination of the right
of the lessee to possession of the property, whichever is the earlier
time.

The landlord seems to be aware of this which is why suit was filed within 4 years. Even if the lease was verbally modified, it would not change the rights as shown for 337.2 in my opinion. You might argue in court, that the breach was part of the verbally modified clauses and therefore would require a short SOL, but I doubt if that would fly.